## I dont understand compound interest.

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SinghJapneet1
Posts: 9
Joined: Tue Sep 22, 2020 10:32 pm

### I dont understand compound interest.

Hello my first time posting sorry if I post in the wrong thread it looked like this one was for general questions. For some reason Im not understanding compound interest. Im reading the book bogleheads guide for investing first edition and it gives a couple examples. One is
At age 25 Eric invest 4000 a month in roth IRA for 10 years then stops. He invested 40,000 total, there is 8 percent average annual return. His IRA is worth \$629,741. How did we get this number 4,000 times 8 percent would 0.08 so 4000 times 0.08 is 320. So it would 320 plus 4,000 which 4,320, and then times that by 40 is 172,800.
mega317
Posts: 4582
Joined: Tue Apr 19, 2016 10:55 am

### Re: I dont understand compound interest.

Welcome.
What you’re missing is that last year’s interest also earns interest the next year. So yes, 4000 x .08 = 320. But the next year it’s 4320 x .08 = 345. More interest than last year on the same initial investment.
Keep asking questions, you’ll be a successful investor.
banx
Posts: 22
Joined: Wed Jan 02, 2013 8:56 pm

### Re: I dont understand compound interest.

Working out the math fully:

Let's start by focusing only on the 4000 invested in the first year. After 1 year it's 4000*1.08 = 4320. After 2 years it's 4320*1.08 = 4665.60, or put another way it's 4000*1.08*1.08 = 4665.60. After 3 years it's 4000*1.08*1.08*1.08 = 4000*(1.08^3) = 5038.85. And so on, so after 40 years it's 4000*(1.08^40) = 86898.06.

The 4000 you invest the second year works the same way, except it's invested for one fewer year. So it's 4000*(1.08^39)=80461.19.

And so on. So your total is 4000*1.08^40 + 4000*1.08^39 + 4000*1.08^38 + 4000*1.08^37 + 4000*1.08^36 + 4000*1.08^35 + 4000*1.08^34 + 4000*1.08^33 + 4000*1.08^32 + 4000*1.08^31, where that last one is what you invest at the beginning on the tenth year, which sits for 31 years.

Put that in a calculator and you get the 629,741.
Miriam2
Posts: 3115
Joined: Fri Nov 14, 2014 11:51 am

### Re: I dont understand compound interest.

mega317 wrote: What you’re missing is that last year’s interest also earns interest the next year. So yes, 4000 x .08 = 320. But the next year it’s 4320 x .08 = 345. More interest than last year on the same initial investment. , , ,
banx wrote: Working out the math fully:

Let's start by focusing only on the 4000 invested in the first year. After 1 year it's 4000*1.08 = 4320. After 2 years it's 4320*1.08 = 4665.60, or put another way it's 4000*1.08*1.08 = 4665.60. After 3 years it's 4000*1.08*1.08*1.08 = 4000*(1.08^3) = 5038.85. And so on, so after 40 years it's 4000*(1.08^40) = 86898.06. . . . .
This is why I read this Forum - simple, easy to understand answers explaining math concepts to those of us who are math challenged I'm not even the original poster, but thank you for these explanations
John Bogle, "The Twelve Pillars of Wisdom" - Pillar 3: Time Marches On. Time dramatically enhances capital accumulation as the magic of compounding accelerates.
ddurrett896
Posts: 1366
Joined: Wed Nov 05, 2014 3:23 pm

### Re: I dont understand compound interest.

It’s like a snowball rolling downhill, picking up more and more snow. The more snow is compound interest and as it gets bigger, it picks up more snow.
billfromct
Posts: 1115
Joined: Tue Dec 03, 2013 9:05 am

### Re: I dont understand compound interest.

Another aspect of compound interest is “the rule of 72”.

If you take an average annual return & divide that number into 72, you get the number of years to double your money.

An average 10% return will double your money in 7.2 years; an average 7% return will double your money in about 10 years.

I think I read somewhere that the S&P 500 & it’s predecessor before 1957, returned an average of 10.2% per year since 1926. I use a conservative 7% stock market return to estimate future stock market gains which would double your money about every 10 years.

Of course, past performance does not guarantee future returns.

bill
Stinky
Posts: 5567
Joined: Mon Jun 12, 2017 11:38 am
Location: Sweet Home Alabama

### Re: I dont understand compound interest.

ddurrett896 wrote: Wed Sep 23, 2020 5:12 am It’s like a snowball rolling downhill, picking up more and more snow. The more snow is compound interest and as it gets bigger, it picks up more snow.
+1

I've always thought that this is one of the analogies that is easiest to understand.
It's a GREAT day to be alive - Travis Tritt
wolf359
Posts: 2199
Joined: Sun Mar 15, 2015 8:47 am

### Re: I dont understand compound interest.

SinghJapneet1 wrote: Tue Sep 22, 2020 10:38 pm Hello my first time posting sorry if I post in the wrong thread it looked like this one was for general questions. For some reason Im not understanding compound interest. Im reading the book bogleheads guide for investing first edition and it gives a couple examples. One is
At age 25 Eric invest 4000 a month in roth IRA for 10 years then stops. He invested 40,000 total, there is 8 percent average annual return. His IRA is worth \$629,741. How did we get this number 4,000 times 8 percent would 0.08 so 4000 times 0.08 is 320. So it would 320 plus 4,000 which 4,320, and then times that by 40 is 172,800.
Singh, did you understand the explanations above, or do you need more?

Compound interest is one of the keys to wealth building. The earlier that you invest your money in an investment vehicle that compounds, the more money you will accumulate. A little money invested early can potentially result in a bigger nest egg than a lot of money invested closer to the goal. (That's the example you were reading.)

Market timing is when you try to predict the market by putting the money in before the market goes up, and taking it out before it drops. It sounds obvious when you look at a stock chart that if you had simply sold at the peaks and bought at the dips that you'd make a lot of money. However, THIS IS A TRAP. In real-time, it is impossible to know where the tops of the peaks and the bottom of the dips are. If you take your money out of the market at the wrong time, you lose the compounding effect. Think of what happened this March. The biggest single negative days of the year were accompanied by the biggest single positive days of the year, all mixed together. Things were volatile, and you had no way to know whether the bulls or bears would win. You accumulate more if you buy regularly all the way through the time period and allow your money to compound. Some of those who sold in March are still out of the market, and missed the entire recovery.

Not all investments compound, and not all do so at the same rate. When you buy stocks and you get dividends, you need to reinvest the dividends or you will negate the compounding effect. Real estate generates rent, and it's difficult to reinvest that immediately into another property. (That's why a lot of Bogleheads like stocks over real estate.) Bonds and savings accounts compound, but their returns are so low that it takes forever. Gold and bitcoin don't compound.

The hardest thing to grasp about compound interest is that in the beginning you can't watch it work in real time. It's akin to watching a flower grow, but this flower may take 10 years or more to blossom. It's aggravating to watch day-to-day as the market fluctuates and your balance barely moves. Worse, the market does not compound up in a straight line like all the compound interest calculators do.

The best approach is to start early, invest regularly, have as high a savings rate as possible for as long as possible. If your savings rate is high enough, it will trump any returns you get on the market. Compound interest kicks in during the later half of your investment career, when your balance is so high that your investment returns are starting to match or exceed your regular income. Be patient, and you will be rewarded.
Last edited by wolf359 on Wed Sep 23, 2020 7:54 am, edited 1 time in total.
Point
Posts: 248
Joined: Mon Jul 10, 2017 9:33 pm

### Re: I dont understand compound interest.

Here is a site with a large number of calculators to explore you can learn a lot by working with these:

nisiprius
Posts: 41993
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

### Re: I dont understand compound interest.

Actually, the example given in the book is pretty complicated to reproduce. I just deleted a long post because I see that I wasn't really following the book example... and neither is anyone else.

Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
MotoTrojan
Posts: 10659
Joined: Wed Feb 01, 2017 8:39 pm

### Re: I dont understand compound interest.

This is my favorite example of just how powerful compounding can be.

Would you rather get \$1M cash today, or \$0.01 and I will double the amount every day for 30 days?

https://www.savingtoinvest.com/power-of ... on-now-or/
nisiprius
Posts: 41993
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

### Re: I dont understand compound interest.

Here is the detailed working for "Eric Early." (Doing the calculation in Excel was easy. Getting Excel to format the narrative was difficult!)

At the start of 1979, he has \$0.00.
He adds \$4,000.00. Now he has \$4,000.00.
During 1980, he earns 8% of \$4,000.00 = \$320.00
At the end of 1980, he has \$4,000.00 + \$320.00 = \$4,320.00.

At the start of 1980, he has \$4,320.00.
He adds \$4,000.00. Now he has \$8,320.00.
During 1981, he earns 8% of \$8,320.00 = \$665.60
At the end of 1981, he has \$8,320.00 + \$665.60 = \$8,985.60.

At the start of 1981, he has \$8,985.60.
He adds \$4,000.00. Now he has \$12,985.60.
During 1982, he earns 8% of \$12,985.60 = \$1,038.85
At the end of 1982, he has \$12,985.60 + \$1,038.85 = \$14,024.45.

At the start of 1982, he has \$14,024.45.
He adds \$4,000.00. Now he has \$18,024.45.
During 1983, he earns 8% of \$18,024.45 = \$1,441.96
At the end of 1983, he has \$18,024.45 + \$1,441.96 = \$19,466.40.

At the start of 1983, he has \$19,466.40.
He adds \$4,000.00. Now he has \$23,466.40.
During 1984, he earns 8% of \$23,466.40 = \$1,877.31
At the end of 1984, he has \$23,466.40 + \$1,877.31 = \$25,343.72.

At the start of 1984, he has \$25,343.72.
He adds \$4,000.00. Now he has \$29,343.72.
During 1985, he earns 8% of \$29,343.72 = \$2,347.50
At the end of 1985, he has \$29,343.72 + \$2,347.50 = \$31,691.21.

At the start of 1985, he has \$31,691.21.
He adds \$4,000.00. Now he has \$35,691.21.
During 1986, he earns 8% of \$35,691.21 = \$2,855.30
At the end of 1986, he has \$35,691.21 + \$2,855.30 = \$38,546.51.

At the start of 1986, he has \$38,546.51.
He adds \$4,000.00. Now he has \$42,546.51.
During 1987, he earns 8% of \$42,546.51 = \$3,403.72
At the end of 1987, he has \$42,546.51 + \$3,403.72 = \$45,950.23.

At the start of 1987, he has \$45,950.23.
He adds \$4,000.00. Now he has \$49,950.23.
During 1988, he earns 8% of \$49,950.23 = \$3,996.02
At the end of 1988, he has \$49,950.23 + \$3,996.02 = \$53,946.25.

At the start of 1988, he has \$53,946.25.
He adds \$4,000.00. Now he has \$57,946.25.
During 1989, he earns 8% of \$57,946.25 = \$4,635.70
At the end of 1989, he has \$57,946.25 + \$4,635.70 = \$62,581.95.

At the start of 1989, he has \$62,581.95.
During 1990, he earns 8% of \$62,581.95 = \$5,006.56
At the end of 1990, he has \$62,581.95 + \$5,006.56 = \$67,588.51.

At the start of 1990, he has \$67,588.51.
During 1991, he earns 8% of \$67,588.51 = \$5,407.08
At the end of 1991, he has \$67,588.51 + \$5,407.08 = \$72,995.59.

At the start of 1991, he has \$72,995.59.
During 1992, he earns 8% of \$72,995.59 = \$5,839.65
At the end of 1992, he has \$72,995.59 + \$5,839.65 = \$78,835.23.

At the start of 1992, he has \$78,835.23.
During 1993, he earns 8% of \$78,835.23 = \$6,306.82
At the end of 1993, he has \$78,835.23 + \$6,306.82 = \$85,142.05.

At the start of 1993, he has \$85,142.05.
During 1994, he earns 8% of \$85,142.05 = \$6,811.36
At the end of 1994, he has \$85,142.05 + \$6,811.36 = \$91,953.42.

At the start of 1994, he has \$91,953.42.
During 1995, he earns 8% of \$91,953.42 = \$7,356.27
At the end of 1995, he has \$91,953.42 + \$7,356.27 = \$99,309.69.

At the start of 1995, he has \$99,309.69.
During 1996, he earns 8% of \$99,309.69 = \$7,944.78
At the end of 1996, he has \$99,309.69 + \$7,944.78 = \$107,254.46.

At the start of 1996, he has \$107,254.46.
During 1997, he earns 8% of \$107,254.46 = \$8,580.36
At the end of 1997, he has \$107,254.46 + \$8,580.36 = \$115,834.82.

At the start of 1997, he has \$115,834.82.
During 1998, he earns 8% of \$115,834.82 = \$9,266.79
At the end of 1998, he has \$115,834.82 + \$9,266.79 = \$125,101.61.

At the start of 1998, he has \$125,101.61.
During 1999, he earns 8% of \$125,101.61 = \$10,008.13
At the end of 1999, he has \$125,101.61 + \$10,008.13 = \$135,109.74.

At the start of 1999, he has \$135,109.74.
During 2000, he earns 8% of \$135,109.74 = \$10,808.78
At the end of 2000, he has \$135,109.74 + \$10,808.78 = \$145,918.51.

At the start of 2000, he has \$145,918.51.
During 2001, he earns 8% of \$145,918.51 = \$11,673.48
At the end of 2001, he has \$145,918.51 + \$11,673.48 = \$157,592.00.

At the start of 2001, he has \$157,592.00.
During 2002, he earns 8% of \$157,592.00 = \$12,607.36
At the end of 2002, he has \$157,592.00 + \$12,607.36 = \$170,199.36.

At the start of 2002, he has \$170,199.36.
During 2003, he earns 8% of \$170,199.36 = \$13,615.95
At the end of 2003, he has \$170,199.36 + \$13,615.95 = \$183,815.30.

At the start of 2003, he has \$183,815.30.
During 2004, he earns 8% of \$183,815.30 = \$14,705.22
At the end of 2004, he has \$183,815.30 + \$14,705.22 = \$198,520.53.

At the start of 2004, he has \$198,520.53.
During 2005, he earns 8% of \$198,520.53 = \$15,881.64
At the end of 2005, he has \$198,520.53 + \$15,881.64 = \$214,402.17.

At the start of 2005, he has \$214,402.17.
During 2006, he earns 8% of \$214,402.17 = \$17,152.17
At the end of 2006, he has \$214,402.17 + \$17,152.17 = \$231,554.34.

At the start of 2006, he has \$231,554.34.
During 2007, he earns 8% of \$231,554.34 = \$18,524.35
At the end of 2007, he has \$231,554.34 + \$18,524.35 = \$250,078.69.

At the start of 2007, he has \$250,078.69.
During 2008, he earns 8% of \$250,078.69 = \$20,006.30
At the end of 2008, he has \$250,078.69 + \$20,006.30 = \$270,084.99.

At the start of 2008, he has \$270,084.99.
During 2009, he earns 8% of \$270,084.99 = \$21,606.80
At the end of 2009, he has \$270,084.99 + \$21,606.80 = \$291,691.79.

At the start of 2009, he has \$291,691.79.
During 2010, he earns 8% of \$291,691.79 = \$23,335.34
At the end of 2010, he has \$291,691.79 + \$23,335.34 = \$315,027.13.

At the start of 2010, he has \$315,027.13.
During 2011, he earns 8% of \$315,027.13 = \$25,202.17
At the end of 2011, he has \$315,027.13 + \$25,202.17 = \$340,229.30.

At the start of 2011, he has \$340,229.30.
During 2012, he earns 8% of \$340,229.30 = \$27,218.34
At the end of 2012, he has \$340,229.30 + \$27,218.34 = \$367,447.64.

At the start of 2012, he has \$367,447.64.
During 2013, he earns 8% of \$367,447.64 = \$29,395.81
At the end of 2013, he has \$367,447.64 + \$29,395.81 = \$396,843.45.

At the start of 2013, he has \$396,843.45.
During 2014, he earns 8% of \$396,843.45 = \$31,747.48
At the end of 2014, he has \$396,843.45 + \$31,747.48 = \$428,590.93.

At the start of 2014, he has \$428,590.93.
During 2015, he earns 8% of \$428,590.93 = \$34,287.27
At the end of 2015, he has \$428,590.93 + \$34,287.27 = \$462,878.21.

At the start of 2015, he has \$462,878.21.
During 2016, he earns 8% of \$462,878.21 = \$37,030.26
At the end of 2016, he has \$462,878.21 + \$37,030.26 = \$499,908.46.

At the start of 2016, he has \$499,908.46.
During 2017, he earns 8% of \$499,908.46 = \$39,992.68
At the end of 2017, he has \$499,908.46 + \$39,992.68 = \$539,901.14.

At the start of 2017, he has \$539,901.14.
During 2018, he earns 8% of \$539,901.14 = \$43,192.09
At the end of 2018, he has \$539,901.14 + \$43,192.09 = \$583,093.23.

At the start of 2018, he has \$583,093.23.
During 2019, he earns 8% of \$583,093.23 = \$46,647.46
At the end of 2019, he has \$583,093.23 + \$46,647.46 = \$629,740.69.
Last edited by nisiprius on Wed Sep 23, 2020 9:00 am, edited 3 times in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
nisiprius
Posts: 41993
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

### Re: I dont understand compound interest.

Here is the detailed working for "Larry Lately."

At the start of 1979, he has \$0.00.
During 1980, he earns 8% of \$0.00 = \$0.00
At the end of 1980, he has \$0.00 + \$0.00 = \$0.00.

At the start of 1980, he has \$0.00.
During 1981, he earns 8% of \$0.00 = \$0.00
At the end of 1981, he has \$0.00 + \$0.00 = \$0.00.

At the start of 1981, he has \$0.00.
During 1982, he earns 8% of \$0.00 = \$0.00
At the end of 1982, he has \$0.00 + \$0.00 = \$0.00.

At the start of 1982, he has \$0.00.
During 1983, he earns 8% of \$0.00 = \$0.00
At the end of 1983, he has \$0.00 + \$0.00 = \$0.00.

At the start of 1983, he has \$0.00.
During 1984, he earns 8% of \$0.00 = \$0.00
At the end of 1984, he has \$0.00 + \$0.00 = \$0.00.

At the start of 1984, he has \$0.00.
During 1985, he earns 8% of \$0.00 = \$0.00
At the end of 1985, he has \$0.00 + \$0.00 = \$0.00.

At the start of 1985, he has \$0.00.
During 1986, he earns 8% of \$0.00 = \$0.00
At the end of 1986, he has \$0.00 + \$0.00 = \$0.00.

At the start of 1986, he has \$0.00.
During 1987, he earns 8% of \$0.00 = \$0.00
At the end of 1987, he has \$0.00 + \$0.00 = \$0.00.

At the start of 1987, he has \$0.00.
During 1988, he earns 8% of \$0.00 = \$0.00
At the end of 1988, he has \$0.00 + \$0.00 = \$0.00.

At the start of 1988, he has \$0.00.
During 1989, he earns 8% of \$0.00 = \$0.00
At the end of 1989, he has \$0.00 + \$0.00 = \$0.00.

At the start of 1989, he has \$0.00.
He adds \$4,000.00. Now he has \$4,000.00.
During 1990, he earns 8% of \$4,000.00 = \$320.00
At the end of 1990, he has \$4,000.00 + \$320.00 = \$4,320.00.

At the start of 1990, he has \$4,320.00.
He adds \$4,000.00. Now he has \$8,320.00.
During 1991, he earns 8% of \$8,320.00 = \$665.60
At the end of 1991, he has \$8,320.00 + \$665.60 = \$8,985.60.

At the start of 1991, he has \$8,985.60.
He adds \$4,000.00. Now he has \$12,985.60.
During 1992, he earns 8% of \$12,985.60 = \$1,038.85
At the end of 1992, he has \$12,985.60 + \$1,038.85 = \$14,024.45.

At the start of 1992, he has \$14,024.45.
He adds \$4,000.00. Now he has \$18,024.45.
During 1993, he earns 8% of \$18,024.45 = \$1,441.96
At the end of 1993, he has \$18,024.45 + \$1,441.96 = \$19,466.40.

At the start of 1993, he has \$19,466.40.
He adds \$4,000.00. Now he has \$23,466.40.
During 1994, he earns 8% of \$23,466.40 = \$1,877.31
At the end of 1994, he has \$23,466.40 + \$1,877.31 = \$25,343.72.

At the start of 1994, he has \$25,343.72.
He adds \$4,000.00. Now he has \$29,343.72.
During 1995, he earns 8% of \$29,343.72 = \$2,347.50
At the end of 1995, he has \$29,343.72 + \$2,347.50 = \$31,691.21.

At the start of 1995, he has \$31,691.21.
He adds \$4,000.00. Now he has \$35,691.21.
During 1996, he earns 8% of \$35,691.21 = \$2,855.30
At the end of 1996, he has \$35,691.21 + \$2,855.30 = \$38,546.51.

At the start of 1996, he has \$38,546.51.
He adds \$4,000.00. Now he has \$42,546.51.
During 1997, he earns 8% of \$42,546.51 = \$3,403.72
At the end of 1997, he has \$42,546.51 + \$3,403.72 = \$45,950.23.

At the start of 1997, he has \$45,950.23.
He adds \$4,000.00. Now he has \$49,950.23.
During 1998, he earns 8% of \$49,950.23 = \$3,996.02
At the end of 1998, he has \$49,950.23 + \$3,996.02 = \$53,946.25.

At the start of 1998, he has \$53,946.25.
He adds \$4,000.00. Now he has \$57,946.25.
During 1999, he earns 8% of \$57,946.25 = \$4,635.70
At the end of 1999, he has \$57,946.25 + \$4,635.70 = \$62,581.95.

At the start of 1999, he has \$62,581.95.
He adds \$4,000.00. Now he has \$66,581.95.
During 2000, he earns 8% of \$66,581.95 = \$5,326.56
At the end of 2000, he has \$66,581.95 + \$5,326.56 = \$71,908.51.

At the start of 2000, he has \$71,908.51.
He adds \$4,000.00. Now he has \$75,908.51.
During 2001, he earns 8% of \$75,908.51 = \$6,072.68
At the end of 2001, he has \$75,908.51 + \$6,072.68 = \$81,981.19.

At the start of 2001, he has \$81,981.19.
He adds \$4,000.00. Now he has \$85,981.19.
During 2002, he earns 8% of \$85,981.19 = \$6,878.49
At the end of 2002, he has \$85,981.19 + \$6,878.49 = \$92,859.68.

At the start of 2002, he has \$92,859.68.
He adds \$4,000.00. Now he has \$96,859.68.
During 2003, he earns 8% of \$96,859.68 = \$7,748.77
At the end of 2003, he has \$96,859.68 + \$7,748.77 = \$104,608.46.

At the start of 2003, he has \$104,608.46.
He adds \$4,000.00. Now he has \$108,608.46.
During 2004, he earns 8% of \$108,608.46 = \$8,688.68
At the end of 2004, he has \$108,608.46 + \$8,688.68 = \$117,297.13.

At the start of 2004, he has \$117,297.13.
He adds \$4,000.00. Now he has \$121,297.13.
During 2005, he earns 8% of \$121,297.13 = \$9,703.77
At the end of 2005, he has \$121,297.13 + \$9,703.77 = \$131,000.90.

At the start of 2005, he has \$131,000.90.
He adds \$4,000.00. Now he has \$135,000.90.
During 2006, he earns 8% of \$135,000.90 = \$10,800.07
At the end of 2006, he has \$135,000.90 + \$10,800.07 = \$145,800.97.

At the start of 2006, he has \$145,800.97.
He adds \$4,000.00. Now he has \$149,800.97.
During 2007, he earns 8% of \$149,800.97 = \$11,984.08
At the end of 2007, he has \$149,800.97 + \$11,984.08 = \$161,785.05.

At the start of 2007, he has \$161,785.05.
He adds \$4,000.00. Now he has \$165,785.05.
During 2008, he earns 8% of \$165,785.05 = \$13,262.80
At the end of 2008, he has \$165,785.05 + \$13,262.80 = \$179,047.86.

At the start of 2008, he has \$179,047.86.
He adds \$4,000.00. Now he has \$183,047.86.
During 2009, he earns 8% of \$183,047.86 = \$14,643.83
At the end of 2009, he has \$183,047.86 + \$14,643.83 = \$197,691.69.

At the start of 2009, he has \$197,691.69.
He adds \$4,000.00. Now he has \$201,691.69.
During 2010, he earns 8% of \$201,691.69 = \$16,135.33
At the end of 2010, he has \$201,691.69 + \$16,135.33 = \$217,827.02.

At the start of 2010, he has \$217,827.02.
He adds \$4,000.00. Now he has \$221,827.02.
During 2011, he earns 8% of \$221,827.02 = \$17,746.16
At the end of 2011, he has \$221,827.02 + \$17,746.16 = \$239,573.18.

At the start of 2011, he has \$239,573.18.
He adds \$4,000.00. Now he has \$243,573.18.
During 2012, he earns 8% of \$243,573.18 = \$19,485.85
At the end of 2012, he has \$243,573.18 + \$19,485.85 = \$263,059.04.

At the start of 2012, he has \$263,059.04.
He adds \$4,000.00. Now he has \$267,059.04.
During 2013, he earns 8% of \$267,059.04 = \$21,364.72
At the end of 2013, he has \$267,059.04 + \$21,364.72 = \$288,423.76.

At the start of 2013, he has \$288,423.76.
He adds \$4,000.00. Now he has \$292,423.76.
During 2014, he earns 8% of \$292,423.76 = \$23,393.90
At the end of 2014, he has \$292,423.76 + \$23,393.90 = \$315,817.66.

At the start of 2014, he has \$315,817.66.
He adds \$4,000.00. Now he has \$319,817.66.
During 2015, he earns 8% of \$319,817.66 = \$25,585.41
At the end of 2015, he has \$319,817.66 + \$25,585.41 = \$345,403.07.

At the start of 2015, he has \$345,403.07.
He adds \$4,000.00. Now he has \$349,403.07.
During 2016, he earns 8% of \$349,403.07 = \$27,952.25
At the end of 2016, he has \$349,403.07 + \$27,952.25 = \$377,355.32.

At the start of 2016, he has \$377,355.32.
He adds \$4,000.00. Now he has \$381,355.32.
During 2017, he earns 8% of \$381,355.32 = \$30,508.43
At the end of 2017, he has \$381,355.32 + \$30,508.43 = \$411,863.74.

At the start of 2017, he has \$411,863.74.
He adds \$4,000.00. Now he has \$415,863.74.
During 2018, he earns 8% of \$415,863.74 = \$33,269.10
At the end of 2018, he has \$415,863.74 + \$33,269.10 = \$449,132.84.

At the start of 2018, he has \$449,132.84.
He adds \$4,000.00. Now he has \$453,132.84.
During 2019, he earns 8% of \$453,132.84 = \$36,250.63
At the end of 2019, he has \$453,132.84 + \$36,250.63 = \$489,383.47.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
dbr
Posts: 33842
Joined: Sun Mar 04, 2007 9:50 am

### Re: I dont understand compound interest.

The above examples are the kind of work you have to do to actually see what is happening. But even those examples don't show in detail some important features such as how large the various payments of interest in each year eventually grow by earning more interest or how much each increment of interest paid on interest grows by earning more interest, column piled on column year by year.

I suppose one could add detail on detail about this by writing out algebraic expressions forever. Probably a person who has never done so should do it once.

I think Nisi already observed that one feature of the examples is that they conflate periodic investing and compounding in the same result. To understand compounding per se it would be better to only invest an initial amount and tabulate how that grows year on year. But the example is a more realistic case from the real world.

Note that the result can be calculated using spreadsheet functions such as Excel FV (future value) though you have to break it into two pieces where the contributions stop.
Topic Author
SinghJapneet1
Posts: 9
Joined: Tue Sep 22, 2020 10:32 pm

### Re: I dont understand compound interest.

banx wrote: Wed Sep 23, 2020 1:06 am Working out the math fully:

Let's start by focusing only on the 4000 invested in the first year. After 1 year it's 4000*1.08 = 4320. After 2 years it's 4320*1.08 = 4665.60, or put another way it's 4000*1.08*1.08 = 4665.60. After 3 years it's 4000*1.08*1.08*1.08 = 4000*(1.08^3) = 5038.85. And so on, so after 40 years it's 4000*(1.08^40) = 86898.06.

The 4000 you invest the second year works the same way, except it's invested for one fewer year. So it's 4000*(1.08^39)=80461.19.

And so on. So your total is 4000*1.08^40 + 4000*1.08^39 + 4000*1.08^38 + 4000*1.08^37 + 4000*1.08^36 + 4000*1.08^35 + 4000*1.08^34 + 4000*1.08^33 + 4000*1.08^32 + 4000*1.08^31, where that last one is what you invest at the beginning on the tenth year, which sits for 31 years.

Put that in a calculator and you get the 629,741.
Thanks a lot that was a nice clear simple explanation and clear it up a lot, I want ahead and followed your math and got the same figure I understand it now. thanks
Last edited by SinghJapneet1 on Wed Sep 23, 2020 9:37 am, edited 1 time in total.
nisiprius
Posts: 41993
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

### Re: I dont understand compound interest.

Also:

Notice that the point is not to show the benefit of compounding as such, but to show how compounding gives an advantage to an early start. Notice that the balances for Eric Early and Larry Lately are exactly the same during their first ten years of contributions.
Last edited by nisiprius on Wed Sep 23, 2020 9:25 am, edited 1 time in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
balbrec2
Posts: 342
Joined: Mon Nov 13, 2017 3:03 pm

### Re: I dont understand compound interest.

SinghJapneet1 wrote: Tue Sep 22, 2020 10:38 pm Hello my first time posting sorry if I post in the wrong thread it looked like this one was for general questions. For some reason Im not understanding compound interest. Im reading the book bogleheads guide for investing first edition and it gives a couple examples. One is
At age 25 Eric invest 4000 a month in roth IRA for 10 years then stops. He invested 40,000 total, there is 8 percent average annual return. His IRA is worth \$629,741. How did we get this number 4,000 times 8 percent would 0.08 so 4000 times 0.08 is 320. So it would 320 plus 4,000 which 4,320, and then times that by 40 is 172,800.
There is an old saying. Those that understand compound interest, earn it. Those that don't, pay it.
Compound interest is such a critical concept that understanding it is extremely important.
The posts here are very good at explaining this.
#Cruncher
Posts: 3057
Joined: Fri May 14, 2010 2:33 am
Location: New York City
Contact:

### Re: I dont understand compound interest.

SinghJapneet1 wrote: Tue Sep 22, 2020 10:38 pm... the book bogleheads guide for investing ... At age 25 Eric invest 4000 a month in roth IRA for 10 years then stops. ... there is 8 percent average annual return. His IRA is worth \$629,741 [after 30 more years]
Note that the passage referred to on page 15 in the section The Magic is in the Compounding says \$4,000 per year, not per month. Be aware that, while assuming 8% growth may have been realistic when the book was published in 2007, many people here would consider it too optimistic today, even for a 100% stock portfolio.
banx wrote: Wed Sep 23, 2020 1:06 amSo your total is 4000*1.08^40 + 4000*1.08^39 + 4000*1.08^38 + 4000*1.08^37 + 4000*1.08^36 + 4000*1.08^35 + 4000*1.08^34 + 4000*1.08^33 + 4000*1.08^32 + 4000*1.08^31, where that last one is what you invest at the beginning on the tenth year, which sits for 31 years. Put that in a calculator and you get the 629,741.
Here is banx's calculation in tabular form:

Code: Select all

``````      Grow    Grows     Cumu-
Year Years       To    lative
---- -----   ------   -------
1    40   86,898    86,898
2    39   80,461   167,359
3    38   74,501   241,860
4    37   68,983   310,843
5    36   63,873   374,716
6    35   59,141   433,857
7    34   54,761   488,617
8    33   50,704   539,322
9    32   46,948   586,270
10    31   43,471   629,741``````
And here we get the same result calculating year-by-year for 40 years. Note how after 9 years the 8% growth adds more to the balance each year than the \$4,000 contribution.

Code: Select all

``Year  Contrib  Growth  Balance``

Code: Select all

``````   0                         0
1    4,000     320    4,320
2    4,000     666    8,986
3    4,000   1,039   14,024
4    4,000   1,442   19,466
5    4,000   1,877   25,344
6    4,000   2,347   31,691
7    4,000   2,855   38,547
8    4,000   3,404   45,950
9    4,000   3,996   53,946
10    4,000   4,636   62,582
11            5,007   67,589
12            5,407   72,996
13            5,840   78,835
14            6,307   85,142
15            6,811   91,953
16            7,356   99,310
17            7,945  107,254
18            8,580  115,835
19            9,267  125,102
20           10,008  135,110
21           10,809  145,919
22           11,673  157,592
23           12,607  170,199
24           13,616  183,815
25           14,705  198,521
26           15,882  214,402
27           17,152  231,554
28           18,524  250,079
29           20,006  270,085
30           21,607  291,692
31           23,335  315,027
32           25,202  340,229
33           27,218  367,448
34           29,396  396,843
35           31,747  428,591
36           34,287  462,878
37           37,030  499,908
38           39,993  539,901
39           43,192  583,093
40           46,647  629,741``````
We also get the same result in one line using Excel's FV function where the "1" parameter indicates contributions are made at the start of the year ("0" to indicate made at the end).
629,741 = -FV(8%, 30, 0, FV(8%, 10, -4000, 0, 1), 1)
bloom2708
Posts: 8177
Joined: Wed Apr 02, 2014 2:08 pm
Location: Fargo, ND

### Re: I dont understand compound interest.

Next is to understand you don't get 8% linear with stocks or bonds.

+8, +1, -3, +14, +0, +4, -8, +27, -12....

Compounding .02% isn't as fun at 8%. That is what my Brick & Mortar bank is paying on money market funds.
"We are here to provoke thoughtfulness, not agree with you." Unknown Boglehead
Topic Author
SinghJapneet1
Posts: 9
Joined: Tue Sep 22, 2020 10:32 pm

### Re: I dont understand compound interest.

wolf359 wrote: Wed Sep 23, 2020 7:51 am
SinghJapneet1 wrote: Tue Sep 22, 2020 10:38 pm Hello my first time posting sorry if I post in the wrong thread it looked like this one was for general questions. For some reason Im not understanding compound interest. Im reading the book bogleheads guide for investing first edition and it gives a couple examples. One is
At age 25 Eric invest 4000 a month in roth IRA for 10 years then stops. He invested 40,000 total, there is 8 percent average annual return. His IRA is worth \$629,741. How did we get this number 4,000 times 8 percent would 0.08 so 4000 times 0.08 is 320. So it would 320 plus 4,000 which 4,320, and then times that by 40 is 172,800.
Singh, did you understand the explanations above, or do you need more?

Compound interest is one of the keys to wealth building. The earlier that you invest your money in an investment vehicle that compounds, the more money you will accumulate. A little money invested early can potentially result in a bigger nest egg than a lot of money invested closer to the goal. (That's the example you were reading.)

Market timing is when you try to predict the market by putting the money in before the market goes up, and taking it out before it drops. It sounds obvious when you look at a stock chart that if you had simply sold at the peaks and bought at the dips that you'd make a lot of money. However, THIS IS A TRAP. In real-time, it is impossible to know where the tops of the peaks and the bottom of the dips are. If you take your money out of the market at the wrong time, you lose the compounding effect. Think of what happened this March. The biggest single negative days of the year were accompanied by the biggest single positive days of the year, all mixed together. Things were volatile, and you had no way to know whether the bulls or bears would win. You accumulate more if you buy regularly all the way through the time period and allow your money to compound. Some of those who sold in March are still out of the market, and missed the entire recovery.

Not all investments compound, and not all do so at the same rate. When you buy stocks and you get dividends, you need to reinvest the dividends or you will negate the compounding effect. Real estate generates rent, and it's difficult to reinvest that immediately into another property. (That's why a lot of Bogleheads like stocks over real estate.) Bonds and savings accounts compound, but their returns are so low that it takes forever. Gold and bitcoin don't compound.

The hardest thing to grasp about compound interest is that in the beginning you can't watch it work in real time. It's akin to watching a flower grow, but this flower may take 10 years or more to blossom. It's aggravating to watch day-to-day as the market fluctuates and your balance barely moves. Worse, the market does not compound up in a straight line like all the compound interest calculators do.

The best approach is to start early, invest regularly, have as high a savings rate as possible for as long as possible. If your savings rate is high enough, it will trump any returns you get on the market. Compound interest kicks in during the later half of your investment career, when your balance is so high that your investment returns are starting to match or exceed your regular income. Be patient, and you will be rewarded.
I understand the math now and how compound interest accumulates, you mentioned how not all interest compound like gold and real estate that is good to know. I always thought real estate was a good investment but there are a lot of issues with tenants etc. Some people invest in gold its value does increase but also can lower, some use it as a backup in case the government fails doomsday theories.

I had a little bit about what happened in March thanks for the advice when that happens with the market does it always recover? Is it best to keep money in the market.
Topic Author
SinghJapneet1
Posts: 9
Joined: Tue Sep 22, 2020 10:32 pm

### Re: I dont understand compound interest.

nisiprius wrote: Wed Sep 23, 2020 8:55 am Here is the detailed working for "Eric Early." (Doing the calculation in Excel was easy. Getting Excel to format the narrative was difficult!)

At the start of 1979, he has \$0.00.
He adds \$4,000.00. Now he has \$4,000.00.
During 1980, he earns 8% of \$4,000.00 = \$320.00
At the end of 1980, he has \$4,000.00 + \$320.00 = \$4,320.00.

At the start of 1980, he has \$4,320.00.
He adds \$4,000.00. Now he has \$8,320.00.
During 1981, he earns 8% of \$8,320.00 = \$665.60
At the end of 1981, he has \$8,320.00 + \$665.60 = \$8,985.60.

At the start of 1981, he has \$8,985.60.
He adds \$4,000.00. Now he has \$12,985.60.
During 1982, he earns 8% of \$12,985.60 = \$1,038.85
At the end of 1982, he has \$12,985.60 + \$1,038.85 = \$14,024.45.

At the start of 1982, he has \$14,024.45.
He adds \$4,000.00. Now he has \$18,024.45.
During 1983, he earns 8% of \$18,024.45 = \$1,441.96
At the end of 1983, he has \$18,024.45 + \$1,441.96 = \$19,466.40.

At the start of 1983, he has \$19,466.40.
He adds \$4,000.00. Now he has \$23,466.40.
During 1984, he earns 8% of \$23,466.40 = \$1,877.31
At the end of 1984, he has \$23,466.40 + \$1,877.31 = \$25,343.72.

At the start of 1984, he has \$25,343.72.
He adds \$4,000.00. Now he has \$29,343.72.
During 1985, he earns 8% of \$29,343.72 = \$2,347.50
At the end of 1985, he has \$29,343.72 + \$2,347.50 = \$31,691.21.

At the start of 1985, he has \$31,691.21.
He adds \$4,000.00. Now he has \$35,691.21.
During 1986, he earns 8% of \$35,691.21 = \$2,855.30
At the end of 1986, he has \$35,691.21 + \$2,855.30 = \$38,546.51.

At the start of 1986, he has \$38,546.51.
He adds \$4,000.00. Now he has \$42,546.51.
During 1987, he earns 8% of \$42,546.51 = \$3,403.72
At the end of 1987, he has \$42,546.51 + \$3,403.72 = \$45,950.23.

At the start of 1987, he has \$45,950.23.
He adds \$4,000.00. Now he has \$49,950.23.
During 1988, he earns 8% of \$49,950.23 = \$3,996.02
At the end of 1988, he has \$49,950.23 + \$3,996.02 = \$53,946.25.

At the start of 1988, he has \$53,946.25.
He adds \$4,000.00. Now he has \$57,946.25.
During 1989, he earns 8% of \$57,946.25 = \$4,635.70
At the end of 1989, he has \$57,946.25 + \$4,635.70 = \$62,581.95.

At the start of 1989, he has \$62,581.95.
During 1990, he earns 8% of \$62,581.95 = \$5,006.56
At the end of 1990, he has \$62,581.95 + \$5,006.56 = \$67,588.51.

At the start of 1990, he has \$67,588.51.
During 1991, he earns 8% of \$67,588.51 = \$5,407.08
At the end of 1991, he has \$67,588.51 + \$5,407.08 = \$72,995.59.

At the start of 1991, he has \$72,995.59.
During 1992, he earns 8% of \$72,995.59 = \$5,839.65
At the end of 1992, he has \$72,995.59 + \$5,839.65 = \$78,835.23.

At the start of 1992, he has \$78,835.23.
During 1993, he earns 8% of \$78,835.23 = \$6,306.82
At the end of 1993, he has \$78,835.23 + \$6,306.82 = \$85,142.05.

At the start of 1993, he has \$85,142.05.
During 1994, he earns 8% of \$85,142.05 = \$6,811.36
At the end of 1994, he has \$85,142.05 + \$6,811.36 = \$91,953.42.

At the start of 1994, he has \$91,953.42.
During 1995, he earns 8% of \$91,953.42 = \$7,356.27
At the end of 1995, he has \$91,953.42 + \$7,356.27 = \$99,309.69.

At the start of 1995, he has \$99,309.69.
During 1996, he earns 8% of \$99,309.69 = \$7,944.78
At the end of 1996, he has \$99,309.69 + \$7,944.78 = \$107,254.46.

At the start of 1996, he has \$107,254.46.
During 1997, he earns 8% of \$107,254.46 = \$8,580.36
At the end of 1997, he has \$107,254.46 + \$8,580.36 = \$115,834.82.

At the start of 1997, he has \$115,834.82.
During 1998, he earns 8% of \$115,834.82 = \$9,266.79
At the end of 1998, he has \$115,834.82 + \$9,266.79 = \$125,101.61.

At the start of 1998, he has \$125,101.61.
During 1999, he earns 8% of \$125,101.61 = \$10,008.13
At the end of 1999, he has \$125,101.61 + \$10,008.13 = \$135,109.74.

At the start of 1999, he has \$135,109.74.
During 2000, he earns 8% of \$135,109.74 = \$10,808.78
At the end of 2000, he has \$135,109.74 + \$10,808.78 = \$145,918.51.

At the start of 2000, he has \$145,918.51.
During 2001, he earns 8% of \$145,918.51 = \$11,673.48
At the end of 2001, he has \$145,918.51 + \$11,673.48 = \$157,592.00.

At the start of 2001, he has \$157,592.00.
During 2002, he earns 8% of \$157,592.00 = \$12,607.36
At the end of 2002, he has \$157,592.00 + \$12,607.36 = \$170,199.36.

At the start of 2002, he has \$170,199.36.
During 2003, he earns 8% of \$170,199.36 = \$13,615.95
At the end of 2003, he has \$170,199.36 + \$13,615.95 = \$183,815.30.

At the start of 2003, he has \$183,815.30.
During 2004, he earns 8% of \$183,815.30 = \$14,705.22
At the end of 2004, he has \$183,815.30 + \$14,705.22 = \$198,520.53.

At the start of 2004, he has \$198,520.53.
During 2005, he earns 8% of \$198,520.53 = \$15,881.64
At the end of 2005, he has \$198,520.53 + \$15,881.64 = \$214,402.17.

At the start of 2005, he has \$214,402.17.
During 2006, he earns 8% of \$214,402.17 = \$17,152.17
At the end of 2006, he has \$214,402.17 + \$17,152.17 = \$231,554.34.

At the start of 2006, he has \$231,554.34.
During 2007, he earns 8% of \$231,554.34 = \$18,524.35
At the end of 2007, he has \$231,554.34 + \$18,524.35 = \$250,078.69.

At the start of 2007, he has \$250,078.69.
During 2008, he earns 8% of \$250,078.69 = \$20,006.30
At the end of 2008, he has \$250,078.69 + \$20,006.30 = \$270,084.99.

At the start of 2008, he has \$270,084.99.
During 2009, he earns 8% of \$270,084.99 = \$21,606.80
At the end of 2009, he has \$270,084.99 + \$21,606.80 = \$291,691.79.

At the start of 2009, he has \$291,691.79.
During 2010, he earns 8% of \$291,691.79 = \$23,335.34
At the end of 2010, he has \$291,691.79 + \$23,335.34 = \$315,027.13.

At the start of 2010, he has \$315,027.13.
During 2011, he earns 8% of \$315,027.13 = \$25,202.17
At the end of 2011, he has \$315,027.13 + \$25,202.17 = \$340,229.30.

At the start of 2011, he has \$340,229.30.
During 2012, he earns 8% of \$340,229.30 = \$27,218.34
At the end of 2012, he has \$340,229.30 + \$27,218.34 = \$367,447.64.

At the start of 2012, he has \$367,447.64.
During 2013, he earns 8% of \$367,447.64 = \$29,395.81
At the end of 2013, he has \$367,447.64 + \$29,395.81 = \$396,843.45.

At the start of 2013, he has \$396,843.45.
During 2014, he earns 8% of \$396,843.45 = \$31,747.48
At the end of 2014, he has \$396,843.45 + \$31,747.48 = \$428,590.93.

At the start of 2014, he has \$428,590.93.
During 2015, he earns 8% of \$428,590.93 = \$34,287.27
At the end of 2015, he has \$428,590.93 + \$34,287.27 = \$462,878.21.

At the start of 2015, he has \$462,878.21.
During 2016, he earns 8% of \$462,878.21 = \$37,030.26
At the end of 2016, he has \$462,878.21 + \$37,030.26 = \$499,908.46.

At the start of 2016, he has \$499,908.46.
During 2017, he earns 8% of \$499,908.46 = \$39,992.68
At the end of 2017, he has \$499,908.46 + \$39,992.68 = \$539,901.14.

At the start of 2017, he has \$539,901.14.
During 2018, he earns 8% of \$539,901.14 = \$43,192.09
At the end of 2018, he has \$539,901.14 + \$43,192.09 = \$583,093.23.

At the start of 2018, he has \$583,093.23.
During 2019, he earns 8% of \$583,093.23 = \$46,647.46
At the end of 2019, he has \$583,093.23 + \$46,647.46 = \$629,740.69.
Thanks for the detailed explanation it was easy to follow and clears it up, your right compound interest really is powerful. In the book they said that's why Albert Einstein said it was the greatest mathematical discovery
dbr
Posts: 33842
Joined: Sun Mar 04, 2007 9:50 am

### Re: I dont understand compound interest.

SinghJapneet1 wrote: Wed Sep 23, 2020 9:36 am

Thanks for the detailed explanation it was easy to follow and clears it up, your right compound interest really is powerful. In the book they said that's why Albert Einstein said it was the greatest mathematical discovery
Try it with a negative interest rate (or the effect of inflation cutting away value) or withdrawals instead of contributions (negative contributions).

Compounded inflation is also very powerful, but not in a good way.
Topic Author
SinghJapneet1
Posts: 9
Joined: Tue Sep 22, 2020 10:32 pm

### Re: I dont understand compound interest.

#Cruncher wrote: Wed Sep 23, 2020 9:24 am
SinghJapneet1 wrote: Tue Sep 22, 2020 10:38 pm... the book bogleheads guide for investing ... At age 25 Eric invest 4000 a month in roth IRA for 10 years then stops. ... there is 8 percent average annual return. His IRA is worth \$629,741 [after 30 more years]
Note that the passage referred to on page 15 in the section The Magic is in the Compounding says \$4,000 per year, not per month. Be aware that, while assuming 8% growth may have been realistic when the book was published in 2007, many people here would consider it too optimistic today, even for a 100% stock portfolio.
banx wrote: Wed Sep 23, 2020 1:06 amSo your total is 4000*1.08^40 + 4000*1.08^39 + 4000*1.08^38 + 4000*1.08^37 + 4000*1.08^36 + 4000*1.08^35 + 4000*1.08^34 + 4000*1.08^33 + 4000*1.08^32 + 4000*1.08^31, where that last one is what you invest at the beginning on the tenth year, which sits for 31 years. Put that in a calculator and you get the 629,741.
Here is banx's calculation in tabular form:

Code: Select all

``````      Grow    Grows     Cumu-
Year Years       To    lative
---- -----   ------   -------
1    40   86,898    86,898
2    39   80,461   167,359
3    38   74,501   241,860
4    37   68,983   310,843
5    36   63,873   374,716
6    35   59,141   433,857
7    34   54,761   488,617
8    33   50,704   539,322
9    32   46,948   586,270
10    31   43,471   629,741``````
And here we get the same result calculating year-by-year for 40 years. Note how after 9 years the 8% growth adds more to the balance each year than the \$4,000 contribution.

Code: Select all

``Year  Contrib  Growth  Balance``

Code: Select all

``````   0                         0
1    4,000     320    4,320
2    4,000     666    8,986
3    4,000   1,039   14,024
4    4,000   1,442   19,466
5    4,000   1,877   25,344
6    4,000   2,347   31,691
7    4,000   2,855   38,547
8    4,000   3,404   45,950
9    4,000   3,996   53,946
10    4,000   4,636   62,582
11            5,007   67,589
12            5,407   72,996
13            5,840   78,835
14            6,307   85,142
15            6,811   91,953
16            7,356   99,310
17            7,945  107,254
18            8,580  115,835
19            9,267  125,102
20           10,008  135,110
21           10,809  145,919
22           11,673  157,592
23           12,607  170,199
24           13,616  183,815
25           14,705  198,521
26           15,882  214,402
27           17,152  231,554
28           18,524  250,079
29           20,006  270,085
30           21,607  291,692
31           23,335  315,027
32           25,202  340,229
33           27,218  367,448
34           29,396  396,843
35           31,747  428,591
36           34,287  462,878
37           37,030  499,908
38           39,993  539,901
39           43,192  583,093
40           46,647  629,741``````
We also get the same result in one line using Excel's FV function where the "1" parameter indicates contributions are made at the start of the year ("0" to indicate made at the end).
629,741 = -FV(8%, 30, 0, FV(8%, 10, -4000, 0, 1), 1)
What do you think is a more realistic compound rate today? excels really useful thanks for the tip on how to do it on excel, its definitely quicker and easier to do it on excel.
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### Re: I dont understand compound interest.

SinghJapneet1 wrote: Wed Sep 23, 2020 9:14 am
banx wrote: Wed Sep 23, 2020 1:06 am Working out the math fully:

Let's start by focusing only on the 4000 invested in the first year. After 1 year it's 4000*1.08 = 4320. After 2 years it's 4320*1.08 = 4665.60, or put another way it's 4000*1.08*1.08 = 4665.60. After 3 years it's 4000*1.08*1.08*1.08 = 4000*(1.08^3) = 5038.85. And so on, so after 40 years it's 4000*(1.08^40) = 86898.06.

The 4000 you invest the second year works the same way, except it's invested for one fewer year. So it's 4000*(1.08^39)=80461.19.

And so on. So your total is 4000*1.08^40 + 4000*1.08^39 + 4000*1.08^38 + 4000*1.08^37 + 4000*1.08^36 + 4000*1.08^35 + 4000*1.08^34 + 4000*1.08^33 + 4000*1.08^32 + 4000*1.08^31, where that last one is what you invest at the beginning on the tenth year, which sits for 31 years.

Put that in a calculator and you get the 629,741.
Thanks a lot that was a nice clear simple explanation and clear it up a lot, I want and ahead and followed your math and got the same figure I understand it now. thanks
Note that the explanation covers TWO things: repeated investing AND compounding. So, although the explanation is clear, it explains more than what your question asked.
1. COMPOUNDING: It is the "raising to the power" that accounts for the compounding (assuming the value being raised is greater than 1). In other words, if there was no yearly return (.08 in this example) there would be no compounding (or nothing to compound).
2. REPEATED INVESTING: Repeating that investment each year (\$4000 in this example) is a summing up a series of compounds and is not compounding in itself.
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### Re: I dont understand compound interest.

Eric Early invested \$4k per year for 10 years @ 8% = \$62,581.95
Calculations using Hewlett Packard 10B financial calculator:
N=10yrs I/yr=8% PV=0 PMT=(\$4,000) compute FV=\$62.581.95
After that point he didn't invest any more out of pocket, so he left the \$62,581.95 invested for 30 years @ 8% = \$629,740.69
Calculations using Hewlett Packard 10B financial calculator:
N=30yrs I/yr=8% PV= (\$62,581.95) PMT=0 compute FV=\$629,740.69

Larry Lately invested \$4k per year for 30 years @ 8% = \$489,383.47
Calculations using Hewlett Packard 10B financial calculator:
N=30yrs I/yr=8% PV=0 PMT=(\$4000) compute FV=\$489,383.47

Add: Even though Eric Early invested less money out of pocket than Larry Lately, he ended up with more money because he compounded his money for a longer period of time.
Last edited by Abe on Wed Sep 23, 2020 2:39 pm, edited 5 times in total.
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Oicuryy
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### Re: I dont understand compound interest.

For the math see Geometric Sequences and Sums.

After 30 years Eric had 291691.78 =(4000*1.08*(1.08^10-1)/(1.08-1))*(1.08^20).
After 30 years Larry had 489383.47 =4000*1.08*(1.08^30-1)/(1.08-1).
But an additional 10 years of compounding at 8% was enough to more than double Eric's amount. 629740.68 =(4000*1.08*(1.08^10-1)/(1.08-1))*(1.08^20)*(1.08^10)

Compounding needs time to do its magic.

Ron
Money is fungible | Abbreviations and Acronyms
alex_686
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### Re: I dont understand compound interest.

SinghJapneet1 wrote: Wed Sep 23, 2020 9:31 am I understand the math now and how compound interest accumulates, you mentioned how not all interest compound like gold and real estate that is good to know. I always thought real estate was a good investment but there are a lot of issues with tenants etc.
Real estate can compound. The standardized way to calculate returns on assets is to assume that any cashflows are immediately reinvested back in the asset. Such as when dividends are reinvested back in the stock.

It is a assumption and as such a simplification. For example, rarely can you reinvest a bond's coupon back at the same yield into a new bond. Real estate is both easier and harder. You can reinvest cash flows to paydown the mortgage on the property. This compounds. This is easy. Or you can take the cashflows and invest in new properties. This is lumpy and hard.

In any case, you have to make some assumption on how you are going to reinvest the cashflows when calculating returns. As such you almost always get some type of compounding interest.

Except gold, which either has no cash flows or negative cash flows. You have to pay for storage.
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Sasquatch1
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### Re: I dont understand compound interest.

SinghJapneet1 wrote: Wed Sep 23, 2020 9:31 am
wolf359 wrote: Wed Sep 23, 2020 7:51 am
SinghJapneet1 wrote: Tue Sep 22, 2020 10:38 pm Hello my first time posting sorry if I post in the wrong thread it looked like this one was for general questions. For some reason Im not understanding compound interest. Im reading the book bogleheads guide for investing first edition and it gives a couple examples. One is
At age 25 Eric invest 4000 a month in roth IRA for 10 years then stops. He invested 40,000 total, there is 8 percent average annual return. His IRA is worth \$629,741. How did we get this number 4,000 times 8 percent would 0.08 so 4000 times 0.08 is 320. So it would 320 plus 4,000 which 4,320, and then times that by 40 is 172,800.
Singh, did you understand the explanations above, or do you need more?

Compound interest is one of the keys to wealth building. The earlier that you invest your money in an investment vehicle that compounds, the more money you will accumulate. A little money invested early can potentially result in a bigger nest egg than a lot of money invested closer to the goal. (That's the example you were reading.)

Market timing is when you try to predict the market by putting the money in before the market goes up, and taking it out before it drops. It sounds obvious when you look at a stock chart that if you had simply sold at the peaks and bought at the dips that you'd make a lot of money. However, THIS IS A TRAP. In real-time, it is impossible to know where the tops of the peaks and the bottom of the dips are. If you take your money out of the market at the wrong time, you lose the compounding effect. Think of what happened this March. The biggest single negative days of the year were accompanied by the biggest single positive days of the year, all mixed together. Things were volatile, and you had no way to know whether the bulls or bears would win. You accumulate more if you buy regularly all the way through the time period and allow your money to compound. Some of those who sold in March are still out of the market, and missed the entire recovery.

Not all investments compound, and not all do so at the same rate. When you buy stocks and you get dividends, you need to reinvest the dividends or you will negate the compounding effect. Real estate generates rent, and it's difficult to reinvest that immediately into another property. (That's why a lot of Bogleheads like stocks over real estate.) Bonds and savings accounts compound, but their returns are so low that it takes forever. Gold and bitcoin don't compound.

The hardest thing to grasp about compound interest is that in the beginning you can't watch it work in real time. It's akin to watching a flower grow, but this flower may take 10 years or more to blossom. It's aggravating to watch day-to-day as the market fluctuates and your balance barely moves. Worse, the market does not compound up in a straight line like all the compound interest calculators do.

The best approach is to start early, invest regularly, have as high a savings rate as possible for as long as possible. If your savings rate is high enough, it will trump any returns you get on the market. Compound interest kicks in during the later half of your investment career, when your balance is so high that your investment returns are starting to match or exceed your regular income. Be patient, and you will be rewarded.
I understand the math now and how compound interest accumulates, you mentioned how not all interest compound like gold and real estate that is good to know. I always thought real estate was a good investment but there are a lot of issues with tenants etc. Some people invest in gold its value does increase but also can lower, some use it as a backup in case the government fails doomsday theories.

I had a little bit about what happened in March thanks for the advice when that happens with the market does it always recover? Is it best to keep money in the market.

Being that almost everything is backed by the market in some way.

If it DONT recover, your money sitting in the bank be in the market isn’t going to be worth anything anyway.
arcticpineapplecorp.
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### Re: I dont understand compound interest.

An example using starting investment of \$100 and compounding at 10% per year (unrealistic perhaps, but using the CAGR for U.S. stock market since 1926: https://personal.vanguard.com/us/insigh ... llocations). This example simply demonstrates the "rule of 72" but shows what's happening each year (as Nisiprius's posts have done)

How long will it take a one time \$100 investment to double if earning 10% annual compounding interest?

be wary though, in real life compounding returns aren't clean and neat like this. Just because the market grew at 10% per year since 1926 doesn't mean you'd have earned 10% year in and year out. Remember the Great Depression?
It's "Stay" the course, not Stray the Course. Buy and Hold works. You should really try it sometime. Get a plan: www.bogleheads.org/wiki/Investment_policy_statement
dbr
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### Re: I dont understand compound interest.

It might be that the really serious objection to the original article in some book is that relative to stock market investing the example uses compound annual average growth rate as if it were a fixed rate of interest on an investment. In an actual market returns are different every year, including negative returns. I understand illustrating a point about the advantages of early investing, but this example also contains the seeds of some serious misunderstanding about how returns behave, specifically to completely ignore risk and the long term implications of risk. By risk in this conversation we would mean the variability of annual returns, measured usually by their standard deviation.

This is a dilemma about whether learners should sip through straws or drink from fire hoses.
Topic Author
SinghJapneet1
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### Re: I dont understand compound interest.

dbr wrote: Wed Sep 23, 2020 11:26 am It might be that the really serious objection to the original article in some book is that relative to stock market investing the example uses compound annual average growth rate as if it were a fixed rate of interest on an investment. In an actual market returns are different every year, including negative returns. I understand illustrating a point about the advantages of early investing, but this example also contains the seeds of some serious misunderstanding about how returns behave, specifically to completely ignore risk and the long term implications of risk. By risk in this conversation we would mean the variability of annual returns, measured usually by their standard deviation.

This is a dilemma about whether learners should sip through straws or drink from fire hoses.
Yeah I agree markets fluctuates it wont return 8% every single year the market for example I believe went down in March then recovered.
Stef
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### Re: I dont understand compound interest.

Compound interest is really fascinating. If we assume 7%/year avg. return:

Person A starts investing with 25, 1k/month.
Person B starts investing with 35, 2.1k/month.

They both end up with 2.5 million in assets with 65.
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### Re: I dont understand compound interest.

Stef wrote: Wed Sep 23, 2020 5:22 pm Compound interest is really fascinating. If we assume 7%/year avg. return:
Person A starts investing [at age] 25, 1k/month.
Person B starts investing [at age] 35, 2.1k/month.
They both end up with 2.5 million in assets [at age] 65.
Correct. The following table shows this along with the results for other growth rate and starting age assumptions:

Code: Select all

``````Row      Col A             Col B   Col C   Col D   Col E   Col F   Col G   Col H   Col I
1              Goal  2,500,000
2            At age         65
3  Periods per year         12
4       When invest          0  (0 = start of period, 1 = end of period)
5  Start Age / Rate         0%      1%      2%      3%      4%      5%      6%      7%
6         20             4,630   3,672   2,872   2,217   1,691   1,276     953     707
7     ==> 25             5,208   4,242   3,418   2,726   2,153   1,686   1,310  [1,012]<==
8         30             5,952   4,978   4,129   3,399   2,778   2,255   1,820   1,461
9     ==> 35             6,944   5,962   5,089   4,320   3,648   3,066   2,565  [2,138] <==
10         40             8,333   7,343   6,445   5,637   4,913   4,268   3,697   3,193
11         45            10,417   9,418   8,497   7,649   6,871   6,161   5,513   4,926
12         50            13,889  12,884  11,938  11,050  10,218   9,440   8,713   8,036``````
Here is the formula in cell B6 that is copied down to row 12 and right to column I. It uses the Excel PMT function. The assumptions in cells B3 and B4 allow it to handle monthly, quarterly, semi-annual, or annual contributions made at either the start or end of each period. (Table above shows case for contributions made at the end of each month.)
4,630 = -PMT((1 + B\$5) ^(1 / \$B\$3) - 1, (\$B\$2 - \$A6) * \$B\$3, 0, \$B\$1, \$B\$4)
tibbitts
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### Re: I dont understand compound interest.

Sasquatch1 wrote: Wed Sep 23, 2020 11:03 am Being that almost everything is backed by the market in some way.

If it DONT recover, your money sitting in the bank be in the market isn’t going to be worth anything anyway.
I don't think that's been the Japan experience.
wolf359
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### Re: I dont understand compound interest.

alex_686 wrote: Wed Sep 23, 2020 10:57 am
SinghJapneet1 wrote: Wed Sep 23, 2020 9:31 am I understand the math now and how compound interest accumulates, you mentioned how not all interest compound like gold and real estate that is good to know. I always thought real estate was a good investment but there are a lot of issues with tenants etc.
Real estate can compound. The standardized way to calculate returns on assets is to assume that any cashflows are immediately reinvested back in the asset. Such as when dividends are reinvested back in the stock.

It is a assumption and as such a simplification. For example, rarely can you reinvest a bond's coupon back at the same yield into a new bond. Real estate is both easier and harder. You can reinvest cash flows to paydown the mortgage on the property. This compounds. This is easy. Or you can take the cashflows and invest in new properties. This is lumpy and hard.

In any case, you have to make some assumption on how you are going to reinvest the cashflows when calculating returns. As such you almost always get some type of compounding interest.

Except gold, which either has no cash flows or negative cash flows. You have to pay for storage.
I'm not sure this is correct.

Definition of Compound Interest from Investopedia:
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.

Using the rent to make the mortgage payments does not add to the principal sum of the property. Although some of the mortgage payment goes to principal, the value of the property does not increase, and the dividend payout (rents) don't increase.

If the rent exceeds the mortgage payment, and some is used to pay down the balance, the total value of the property still does not change. The rent does not change. Thus, by the definition of compound interest, no compounding occurred. You're reducing the amount you owe, and but you're not achieving a compounding effect. You're saving money, but it's only the interest on the loan, and you only get it at the end of the mortgage term. Changes in your cost basis (equity) don't increase the overall principal value of the asset.

If the rent exceeds the mortgage payment and you use that excess to improve the property, thus increasing its value or increasing the rent that can be charged, then you're getting the real estate to compound. And of course, buying another property will also create the compounding effect, but that doesn't occur until enough funds are accumulated to purchase more property. But with both these real estate examples, getting the compounding effect is more difficult. It's not quite as easy as just using the rent to pay the mortgage or even pay it down.
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### Re: I dont understand compound interest.

I do think the "wonder" of compound interest is oversold, though. It's so easy to look at a chart and say "If only I had put \$10,000 into the Vanguard 500 Index Fund in 1976, I'd have almost a million dollars today."

This a) the compounding of the inflation rate, and b) the compounding of bad luck.

Inflation is sort of understood, but rarely mentioned when explaining "compounding" to beginners. In 1976 I was making \$3,000 a year on a graduate student fellowship. Investing \$10,000 into the Wellington Fund wasn't practical. \$10,000 then was the rough equivalent of \$44,000 today.

An 8% rate of return for the stock market is easy. An 8% rate of return for a 60/40 balanced portfolio is reasonable; Vanguard Balanced Index Fund has achieved 8.40% since inception, the Vanguard Wellington Fund has achieved 8.2% over the full 91 years since inception.

8% real, for stocks alone or for 60/40 balanced portfolios, is out of the question.

b) is more interesting to consider. You look at these charts and think "everybody ought to be rich." But that's only because it sounds as if it would be such an easy thing to do. It's like the story of Milo of Croton, who "simply" picked up and lifted a calf every day, the same calf, and in a couple of years he was able to lift a full-grown bull. It sounds like something anyone could do.

Maybe what these charts prove is that it is practically impossible to "simply" buy and hold for every long periods of time, because stuff happens.

I used the phrase "everybody ought to be rich" because that was the title of a famous magazine article, an interview with John Jakob Raskob. He argued that someone who invests \$15 a month "in good common stocks and allows the dividends and rights to accumulate" would reach financial independence in twenty years. One reason the article is so famous is that it was published in September, 1929.

So I don't know how to begin to get an actual number on this, but the cumulative compounding of possible failure is just as impressive as the compounding of return. If you have a 95% probability successfully holding for a year, then you only have a 13% chance of managing to hold for forty years.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
dbr
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### Re: I dont understand compound interest.

nisiprius wrote: Thu Sep 24, 2020 11:54 am I do think the "wonder" of compound interest is oversold, though. It's so easy to look at a chart and say "If only I had put \$10,000 into the Vanguard 500 Index Fund in 1976, I'd have almost a million dollars today."

Exactly so. As I tried to mention in a previous post the more relevant compounding for actual investments in the market is the compounding of uncertainty of outcome as discussed in Norstad's famous article about risk and time: https://danluu.com/norstad/risk-time/

The compounding of inflation has hideous consequences for those victimized by it.

As an aside, some of the more relevant examples of compounding apply to decay, such as the decay of radioactivity or the time to clear the body of a drug or contaminant, such as alcohol. A very timely model is the one regarding spread of disease in a population as determined by the reproduction number. These examples are not necessarily "wonders" but perhaps the opposite.
helloeveryone
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### Re: I dont understand compound interest.

SinghJapneet1 wrote: Tue Sep 22, 2020 10:38 pm Hello my first time posting sorry if I post in the wrong thread it looked like this one was for general questions. For some reason Im not understanding compound interest. Im reading the book bogleheads guide for investing first edition and it gives a couple examples. One is
At age 25 Eric invest 4000 a month in roth IRA for 10 years then stops. He invested 40,000 total, there is 8 percent average annual return. His IRA is worth \$629,741. How did we get this number 4,000 times 8 percent would 0.08 so 4000 times 0.08 is 320. So it would 320 plus 4,000 which 4,320, and then times that by 40 is 172,800.
As others have noted - keep educating yourself... and in the meantime contribute to your retirement account. I'm about 16 years into my retirement savings journey (the last 11 years have really been the bulk of being able to maximize my retirement contributions) and am finally truly understanding the power of compounding - the line I look at that makes me really happy I have been doing this is the line item in my statement titled "Dividends and Interests" - that number after 16 years is like "free money" - in that it's money that I'm not working for that is being deposited into my 401k to reinvest and compound further. The year to date number looks great, and when I play with the statement period the 10 year period number is even more amazing to look at.

Although the "change in account value" is amazing to look at as well during these times - it really doesn't mean anything to me since I am not retiring for another 15-20 years.
alex_686
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### Re: I dont understand compound interest.

wolf359 wrote: Thu Sep 24, 2020 11:42 am Definition of Compound Interest from Investopedia:
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
I will quibble with Investopedia's return.

If you use that definition then the only asset class that has compounding interest is coupon bonds.

Stocks don't grow with compound interest then either.

A zero coupon bond would not qualify because it has no coupons. Yet it value increase exponential.

Yet for coupon bonds, zero coupon bonds, stocks, or real estate we calculate return using either the Internal Rate of Return or Time-Weighted Rate of Return which assumes exponential growth. And how is exponential growth different than compounding interest? Critically, when calculating coupon paying bonds we have to make some assumption on cash flow reinvestment, which leads us back to some type of exponential calculation.

Specifically to real estate.

Real estate value and rents tend to track inflation, and that is a exponential calculation. If we have 10 years of inflation we expect the values to change by 1.02^10, not 1.02 * 10.

Next, how do account for cash flows? As a counterpoint, thinks about stocks. Does a stock's return differ if a individual takes cash out as a dividend or reinvests? Does the performance differ between 2 different individuals if one investor did a partial sale and the other did not? No - the stock's performance should be the same in all cases. So, how do you account for rents? Under any legitimate format that I know of - and I know the regulatory approved formats - we are going to end up using some type of exponential calculation.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
bertilak
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### Re: I dont understand compound interest.

alex_686 wrote: Thu Sep 24, 2020 12:55 pm
wolf359 wrote: Thu Sep 24, 2020 11:42 am Definition of Compound Interest from Investopedia:
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
I will quibble with Investopedia's return.

If you use that definition then the only asset class that has compounding interest is coupon bonds.
Is there nothing else that pays interest? What about a bank savings account?

Stocks don't grow with compound interest then either.

A zero coupon bond would not qualify because it has no coupons. Yet it value increase exponential.

Yet for coupon bonds, zero coupon bonds, stocks, or real estate we calculate return using either the Internal Rate of Return or Time-Weighted Rate of Return which assumes exponential growth. And how is exponential growth different than compounding interest? Critically, when calculating coupon paying bonds we have to make some assumption on cash flow reinvestment, which leads us back to some type of exponential calculation.
Anything that does not pay interest can not compound (the non existent) interest.

Specifically to real estate.

Real estate value and rents tend to track inflation, and that is a exponential calculation. If we have 10 years of inflation we expect the values to change by 1.02^10, not 1.02 * 10.

Next, how do account for cash flows? As a counterpoint, thinks about stocks. Does a stock's return differ if a individual takes cash out as a dividend or reinvests? Does the performance differ between 2 different individuals if one investor did a partial sale and the other did not? No - the stock's performance should be the same in all cases. So, how do you account for rents? Under any legitimate format that I know of - and I know the regulatory approved formats - we are going to end up using some type of exponential calculation.
Sure, you can talk about things other than interest that compound, but that is not compound interest. A company's growth can compound if that growth (presumably earnings) is fed back into the company and presuming the company can put it to productive use so that its earnings grow in the future.
May neither drought nor rain nor blizzard disturb the joy juice in your gizzard. -- Squire Omar Barker (aka S.O.B.), the Cowboy Poet
FireAway
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### Re: I dont understand compound interest.

You guys missed the most important lesson from this word problem, which is: Invest in something which pays 8% year after year for the lifetime of your investment.
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SinghJapneet1
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### Re: I dont understand compound interest.

FireAway wrote: Thu Sep 24, 2020 2:41 pm You guys missed the most important lesson from this word problem, which is: Invest in something which pays 8% year after year for the lifetime of your investment.
And what would that be?
Topic Author
SinghJapneet1
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### Re: I dont understand compound interest.

nisiprius wrote: Thu Sep 24, 2020 11:54 am I do think the "wonder" of compound interest is oversold, though. It's so easy to look at a chart and say "If only I had put \$10,000 into the Vanguard 500 Index Fund in 1976, I'd have almost a million dollars today."

This a) the compounding of the inflation rate, and b) the compounding of bad luck.

Inflation is sort of understood, but rarely mentioned when explaining "compounding" to beginners. In 1976 I was making \$3,000 a year on a graduate student fellowship. Investing \$10,000 into the Wellington Fund wasn't practical. \$10,000 then was the rough equivalent of \$44,000 today.

An 8% rate of return for the stock market is easy. An 8% rate of return for a 60/40 balanced portfolio is reasonable; Vanguard Balanced Index Fund has achieved 8.40% since inception, the Vanguard Wellington Fund has achieved 8.2% over the full 91 years since inception.

8% real, for stocks alone or for 60/40 balanced portfolios, is out of the question.

b) is more interesting to consider. You look at these charts and think "everybody ought to be rich." But that's only because it sounds as if it would be such an easy thing to do. It's like the story of Milo of Croton, who "simply" picked up and lifted a calf every day, the same calf, and in a couple of years he was able to lift a full-grown bull. It sounds like something anyone could do.

Maybe what these charts prove is that it is practically impossible to "simply" buy and hold for every long periods of time, because stuff happens.

I used the phrase "everybody ought to be rich" because that was the title of a famous magazine article, an interview with John Jakob Raskob. He argued that someone who invests \$15 a month "in good common stocks and allows the dividends and rights to accumulate" would reach financial independence in twenty years. One reason the article is so famous is that it was published in September, 1929.

So I don't know how to begin to get an actual number on this, but the cumulative compounding of possible failure is just as impressive as the compounding of return. If you have a 95% probability successfully holding for a year, then you only have a 13% chance of managing to hold for forty years.
I agree it is kind of hard to hold the money for that long but if you were is 8% a realistic figure of compound interest per year, you mentioned vanguard was able to keep this rate. If you invest a little were as you can invest it and not worry about it when you retire would you be able to get to a million in savings.
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SinghJapneet1
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### Re: I dont understand compound interest.

helloeveryone wrote: Thu Sep 24, 2020 12:25 pm
SinghJapneet1 wrote: Tue Sep 22, 2020 10:38 pm Hello my first time posting sorry if I post in the wrong thread it looked like this one was for general questions. For some reason Im not understanding compound interest. Im reading the book bogleheads guide for investing first edition and it gives a couple examples. One is
At age 25 Eric invest 4000 a month in roth IRA for 10 years then stops. He invested 40,000 total, there is 8 percent average annual return. His IRA is worth \$629,741. How did we get this number 4,000 times 8 percent would 0.08 so 4000 times 0.08 is 320. So it would 320 plus 4,000 which 4,320, and then times that by 40 is 172,800.
As others have noted - keep educating yourself... and in the meantime contribute to your retirement account. I'm about 16 years into my retirement savings journey (the last 11 years have really been the bulk of being able to maximize my retirement contributions) and am finally truly understanding the power of compounding - the line I look at that makes me really happy I have been doing this is the line item in my statement titled "Dividends and Interests" - that number after 16 years is like "free money" - in that it's money that I'm not working for that is being deposited into my 401k to reinvest and compound further. The year to date number looks great, and when I play with the statement period the 10 year period number is even more amazing to look at.

Although the "change in account value" is amazing to look at as well during these times - it really doesn't mean anything to me since I am not retiring for another 15-20 years.
Thanks for the advice since you have been doing it for 16 years have you seen the market go down and you amount lower and then recover once the market was good again. For example this year I believe market went down in March then recovered.
Sasquatch1
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### Re: I dont understand compound interest.

tibbitts wrote: Thu Sep 24, 2020 11:35 am
Sasquatch1 wrote: Wed Sep 23, 2020 11:03 am Being that almost everything is backed by the market in some way.

If it DONT recover, your money sitting in the bank be in the market isn’t going to be worth anything anyway.
I don't think that's been the Japan experience.
I’m not fully sure how everything their works.

Is their dollar backed by the markets and bonds? Is their retirements in the market? Pensions backed by market? Etc etc.
helloeveryone
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### Re: I dont understand compound interest.

SinghJapneet1 wrote: Thu Sep 24, 2020 3:26 pm
helloeveryone wrote: Thu Sep 24, 2020 12:25 pm
SinghJapneet1 wrote: Tue Sep 22, 2020 10:38 pm Hello my first time posting sorry if I post in the wrong thread it looked like this one was for general questions. For some reason Im not understanding compound interest. Im reading the book bogleheads guide for investing first edition and it gives a couple examples. One is
At age 25 Eric invest 4000 a month in roth IRA for 10 years then stops. He invested 40,000 total, there is 8 percent average annual return. His IRA is worth \$629,741. How did we get this number 4,000 times 8 percent would 0.08 so 4000 times 0.08 is 320. So it would 320 plus 4,000 which 4,320, and then times that by 40 is 172,800.
As others have noted - keep educating yourself... and in the meantime contribute to your retirement account. I'm about 16 years into my retirement savings journey (the last 11 years have really been the bulk of being able to maximize my retirement contributions) and am finally truly understanding the power of compounding - the line I look at that makes me really happy I have been doing this is the line item in my statement titled "Dividends and Interests" - that number after 16 years is like "free money" - in that it's money that I'm not working for that is being deposited into my 401k to reinvest and compound further. The year to date number looks great, and when I play with the statement period the 10 year period number is even more amazing to look at.

Although the "change in account value" is amazing to look at as well during these times - it really doesn't mean anything to me since I am not retiring for another 15-20 years.
Thanks for the advice since you have been doing it for 16 years have you seen the market go down and you amount lower and then recover once the market was good again. For example this year I believe market went down in March then recovered.
Not perfect by any means but thankfully I follow the BH forum all the time and keeps me honest.
sschullo
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### Re: I dont understand compound interest.

MotoTrojan wrote: Wed Sep 23, 2020 8:24 am This is my favorite example of just how powerful compounding can be.

Would you rather get \$1M cash today, or \$0.01 and I will double the amount every day for 30 days?

https://www.savingtoinvest.com/power-of ... on-now-or/
I like the one penny compounded 100% a day too for 30 days. However, I took it up a notch or two.
In 1994 I started with a real stock and bond portfolio with about \$238000. Just for fun, I calculated 100% per day for 30 days starting with \$238,000 and my calculator went up in smoke. It was something like \$300 Trillion at 30 days!
Of course, 100% a day return is just about impossible for any investment as it would bankrupt the world's economies.
"We have seen much more money made and kept by “ordinary people” who were temperamentally well suited for the investment process than by those who lacked this quality." Ben Graham
MotoTrojan
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### Re: I dont understand compound interest.

sschullo wrote: Thu Sep 24, 2020 9:58 pm
MotoTrojan wrote: Wed Sep 23, 2020 8:24 am This is my favorite example of just how powerful compounding can be.

Would you rather get \$1M cash today, or \$0.01 and I will double the amount every day for 30 days?

https://www.savingtoinvest.com/power-of ... on-now-or/
I like the one penny compounded 100% a day too for 30 days. However, I took it up a notch or two.
In 1994 I started with a real stock and bond portfolio with about \$238000. Just for fun, I calculated 100% per day for 30 days starting with \$238,000 and my calculator went up in smoke. It was something like \$300 Trillion at 30 days!
Of course, 100% a day return is just about impossible for any investment as it would bankrupt the world's economies.
Really makes your head spin when you realize that for just over 30 years Jim Simons has had an annual compound of 66% (39% after fees). Sure it isn't 100% or daily, but still unreal growth.