Poll--especially for newbies--financial calc skills?
- nisiprius
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Poll--especially for newbies--financial calc skills?
ADDED: My apologies to two early birds, I had to correct a bad typo in the poll and that erased the early results, please repeat your vote.
ADDED: I did not word the question well. There are two correct answers, corresponding to two different interpretations of the the question, 0.95% and 0.91%.
It just occurred to me to wonder what degree of skill forum members might have in performing financial calculations. I hope people will answer honestly and that the people who actually aren't too sure won't hold back. Eventually when the poll seems to have run its course I, and likely others, will post methods for doing this calculation.
In another post, I looked at some numbers in an article by John Bogle and extracted some numbers, which I will present this way:
1) Benjamin Franklin invested $1,000 for 200 years in a fund he set up in Boston and judged that it would grow to $31,000,000.
2) It actually grew to $5 million.
3) I calculate that, annualized, this represents a shortfall of 0.9% per year. If we pretend that the numbers are precise, a more precise calculation is 0.908126% per year.
That is to say, in the same ballpark as many mutual fund expense ratios. Just as a clue if you choose to check my calculation,
So, I'm curious to know... just how comfortable are people with compound interest calculations?
The poll lets you check multiple answers in this poll, and change your answers after voting. so I ask only to choose answers that are mutually consistent.
Please EVERYBODY check the last checkbox, "I am answering this poll" as it's the only way to figure out how many people voted when multiple answers are allowed.
If I screwed up because you don't like my problem statement or the way I used the word "annualized" or didn't allow for 360-day years or something, then by all means mention so in a reply, but for purposes of answering the poll please stick to the calculation. Just read it as your average mediocre school quiz question. [Added]That was a good disclaimer to make. Maybe I unconsciously sensed that I hadn't written the question well.
ADDED: I did not word the question well. There are two correct answers, corresponding to two different interpretations of the the question, 0.95% and 0.91%.
It just occurred to me to wonder what degree of skill forum members might have in performing financial calculations. I hope people will answer honestly and that the people who actually aren't too sure won't hold back. Eventually when the poll seems to have run its course I, and likely others, will post methods for doing this calculation.
In another post, I looked at some numbers in an article by John Bogle and extracted some numbers, which I will present this way:
1) Benjamin Franklin invested $1,000 for 200 years in a fund he set up in Boston and judged that it would grow to $31,000,000.
2) It actually grew to $5 million.
3) I calculate that, annualized, this represents a shortfall of 0.9% per year. If we pretend that the numbers are precise, a more precise calculation is 0.908126% per year.
That is to say, in the same ballpark as many mutual fund expense ratios. Just as a clue if you choose to check my calculation,
So, I'm curious to know... just how comfortable are people with compound interest calculations?
The poll lets you check multiple answers in this poll, and change your answers after voting. so I ask only to choose answers that are mutually consistent.
Please EVERYBODY check the last checkbox, "I am answering this poll" as it's the only way to figure out how many people voted when multiple answers are allowed.
If I screwed up because you don't like my problem statement or the way I used the word "annualized" or didn't allow for 360-day years or something, then by all means mention so in a reply, but for purposes of answering the poll please stick to the calculation. Just read it as your average mediocre school quiz question. [Added]That was a good disclaimer to make. Maybe I unconsciously sensed that I hadn't written the question well.
Last edited by nisiprius on Mon Feb 03, 2014 8:57 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.
- frugaltype
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Re: Poll--especially for newbies--financial calc skills?
I know how to do this in BASIC, not in Excel, but I didn't bother to install BASIC and do it
Update: I couldn't resist:
.05307 gets 31,006,171
.04354 gets 5,032,921
difference in interest rate is 0.95%
Usual blathering about rounding errors and how precise I was willing to get.
Update: I couldn't resist:
.05307 gets 31,006,171
.04354 gets 5,032,921
difference in interest rate is 0.95%
Usual blathering about rounding errors and how precise I was willing to get.
Last edited by frugaltype on Mon Feb 03, 2014 8:03 am, edited 3 times in total.
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Re: Poll--especially for newbies--financial calc skills?
I used a financial calculator which I considered a pocket calculator. I did not get your precise answer but pretty close. I will chalk it up to rounding over 200 years.
Re: Poll--especially for newbies--financial calc skills?
Should we consider approx. 0.95% the same answer as the OP's 0.91%?frugaltype wrote:I know how to do this in BASIC, not in Excel, but I didn't bother to install BASIC and do it
Update: I couldn't resist:
.05307 gets 31,006,171
.04354 gets 5,032,921
difference in interest rate is 0.95%
Usual blathering about rounding errors and how precise I was willing to get.
Re: Poll--especially for newbies--financial calc skills?
Well I nearly got the same answer as you.
I did this three different ways.
1) I used the function fv = pv *(1+i)^nper and I solved for 'i' in both cases. Here I got a difference of .9563%
2) I set up an "xirr" calculation in Excel (1/1/2000 to 1/1/2200) and I got a difference of .9556% in final rate of return.
3) I set up a "rate" calculation in Excel with 200 as the number of periods and I got a difference of .9563% which was the same result as in #1 above.
So I am not really sure how to account for the difference between my answer and your answer.
I did this three different ways.
1) I used the function fv = pv *(1+i)^nper and I solved for 'i' in both cases. Here I got a difference of .9563%
2) I set up an "xirr" calculation in Excel (1/1/2000 to 1/1/2200) and I got a difference of .9556% in final rate of return.
3) I set up a "rate" calculation in Excel with 200 as the number of periods and I got a difference of .9563% which was the same result as in #1 above.
So I am not really sure how to account for the difference between my answer and your answer.
Re: Poll--especially for newbies--financial calc skills?
My answer (using an HP10B) is exactly the same as yours. I too wasn't sure how to respond to the poll (is a .96 difference "completely" different from the OPs answer)?red5 wrote:Well I nearly got the same answer as you.
I did this three different ways.
1) I used the function fv = pv *(1+i)^nper and I solved for 'i' in both cases. Here I got a difference of .9563%
2) I set up an "xirr" calculation in Excel (1/1/2000 to 1/1/2200) and I got a difference of .9556% in final rate of return.
3) I set up a "rate" calculation in Excel with 200 as the number of periods and I got a difference of .9563% which was the same result as in #1 above.
So I am not really sure how to account for the difference between my answer and your answer.
Now I'm wondering whether there is an "issue" with financial calculators or whether there are a pack of people out there who have calculators which get the, uniformly, wrong answer?
Last edited by dkturner on Mon Feb 03, 2014 8:39 am, edited 1 time in total.
Re: Poll--especially for newbies--financial calc skills?
I figured out how you got your number but I'm not sure why this is a good number to call the "shortfall". I'm hoping to have that explained to me as the thread develops.
Re: Poll--especially for newbies--financial calc skills?
Well, I found a number around 0.95% too, but a tiny bit more, actually, so this would round up to 1.0%, not 0.9%. So I voted that the OP 'messed up'. Ok, acting a tad tongue-in-cheek, I'll admit.richard wrote:Should we consider approx. 0.95% the same answer as the OP's 0.91%?frugaltype wrote:I know how to do this in BASIC, not in Excel, but I didn't bother to install BASIC and do it
Update: I couldn't resist:
.05307 gets 31,006,171
.04354 gets 5,032,921
difference in interest rate is 0.95%
Usual blathering about rounding errors and how precise I was willing to get.
PS. I was using an Excel line-by-line computation as I always do.
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Re: Poll--especially for newbies--financial calc skills?
I did. It was clear from the wording that we were working with round numbers.richard wrote:Should we consider approx. 0.95% the same answer as the OP's 0.91%?frugaltype wrote:I know how to do this in BASIC, not in Excel, but I didn't bother to install BASIC and do it
Update: I couldn't resist:
.05307 gets 31,006,171
.04354 gets 5,032,921
difference in interest rate is 0.95%
Usual blathering about rounding errors and how precise I was willing to get.
- nisiprius
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Re: Poll--especially for newbies--financial calc skills?
+1guymo wrote:I figured out how you got your number but I'm not sure why this is a good number to call the "shortfall". I'm hoping to have that explained to me as the thread develops.
I probably should not have called it that.
No, we shouldn't, 0.95% versus 0.91% isn't rounding error. This is pretty interesting. I won't argue with anyone who says I was wrong. I definitely failed to word the problem unambiguously. 0.95% and 0.91% are both correct answers to slightly different questions.red5 wrote:Should we consider approx. 0.95% the same answer as the OP's 0.91%?
The people who are getting 0.95% calculated the interest rates and took the arithmetic difference.
The people who are getting 0.91% took the ratio between the actual and hoped-for numbers and annualized it.
In my opinion, each of these is correct answers to each of two reasonable questions.
This is going to be an interesting discussion. I'm just going to use all the significant digits the Mac OS X calculator applet calculates:
$1000 -> $31,000,000 = 5.306895192401%
$1000 -> $5,000,000 = 4.350575848921%
5.306895192401% MINUS 4.350575848921% = 0.95631934348% as others stated. The difference in expected and achieved interest rates is 0.956%
But, 104.3505758481% / 105.306895192401% = 0.99091873953996 = 99.091873953996%. [Added: This line has been corrected, was 4.3505758481% / 5.306895192401%]
That is, the annual interest achieved was 99.091873953996 of that expected, which I then chose to describe as a "shortfall" of 0.908126046004%.
In other words... I worded things badly and/or screwed up in minor way.
Let me see whether I can write a question to which "0.908%" is the correct answer: "A certain investment A earns exactly the same percentage in interest every year for 200 years. If the investment trust had no fees, $1,000 would grow to $31,000,000 in 200 years. Every year, however, the managers take a fee of X% of the assets. If $1,000 actually grows to only $5,000,000 in 200 years, how large is X?"
Last edited by nisiprius on Mon Feb 03, 2014 11:26 am, edited 2 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.
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Re: Poll--especially for newbies--financial calc skills?
Now I would retract my answer and say you messed up. .095 is more correct that .091.
You are acting as if the effect of the fee is somehow multiplicative each year, but it is only additive. To get the realized return, you subtract the fee, as a percentage of assets, from the non-fee return, for each year. The effect compounds over time geometrically, but for any one year the effect is strictly additive.
But part of me wonders if this is an elaborate snare you've set for us.
You are acting as if the effect of the fee is somehow multiplicative each year, but it is only additive. To get the realized return, you subtract the fee, as a percentage of assets, from the non-fee return, for each year. The effect compounds over time geometrically, but for any one year the effect is strictly additive.
But part of me wonders if this is an elaborate snare you've set for us.
Re: Poll--especially for newbies--financial calc skills?
I matched nisiprius' numbers. Here's how I did it, without worrying about the growth rate.
If you expected $31M and wound up with $5M, you lost a factor of 6.2. What compound interest rate would destroy a factor of 6.2 over 200 years?
Answer: (1/6.2)^(1/200)=.9909187395 is the rate of change; subtracting this from 1 gives an interest rate of negative .0090812605.
So, if you have an investment for 200 years, and every year, the expenses consume .908% of the investment value, you will wind up with $5M if a zero-cost investment would have earned $31M.
To get the .952% answer, you have to deduct the expenses from the returns rather than compounding them. With no expenses, the growth rate would have been 5.307%; with expenses, the growth rate is 4.351%. The difference between these two numbers is 0.952%.
I believe the .908% is the correct answer because of the way compounding works. If you gain 5.307% and then lose 0.908%, your net gain is 4.351%. This is how you would report the numbers if you had the gain and loss in different time periods, so it makes just as much sense if you have the same gain and loss. And it also corresponds to how investments actually work; the expense ratio of your fund is charged on the current investment balance, not on the amount you had in the fund on the first day of the year.
If you expected $31M and wound up with $5M, you lost a factor of 6.2. What compound interest rate would destroy a factor of 6.2 over 200 years?
Answer: (1/6.2)^(1/200)=.9909187395 is the rate of change; subtracting this from 1 gives an interest rate of negative .0090812605.
So, if you have an investment for 200 years, and every year, the expenses consume .908% of the investment value, you will wind up with $5M if a zero-cost investment would have earned $31M.
To get the .952% answer, you have to deduct the expenses from the returns rather than compounding them. With no expenses, the growth rate would have been 5.307%; with expenses, the growth rate is 4.351%. The difference between these two numbers is 0.952%.
I believe the .908% is the correct answer because of the way compounding works. If you gain 5.307% and then lose 0.908%, your net gain is 4.351%. This is how you would report the numbers if you had the gain and loss in different time periods, so it makes just as much sense if you have the same gain and loss. And it also corresponds to how investments actually work; the expense ratio of your fund is charged on the current investment balance, not on the amount you had in the fund on the first day of the year.
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Re: Poll--especially for newbies--financial calc skills?
This is why I hate computer graded tests. We all would have flunked.nisiprius wrote:ADDED: I did not word the question well. There are two correct answers, corresponding to two different interpretations of the the question, 0.95% and 0.91%.
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Re: Poll--especially for newbies--financial calc skills?
No. There's nothing subtle here. It really is going to be an interesting discussion. I meant this to be an easy and straightforward calculation. If I had been trying for the subtle point, the poll questions would have included both the 0.95% and the 0.91% answers.Aptenodytes wrote:Now I would retract my answer and say you messed up. .095 is more correct that .091.
You are acting as if the effect of the fee is somehow multiplicative each year, but it is only additive. To get the realized return, you subtract the fee, as a percentage of assets, from the non-fee return, for each year. The effect compounds over time geometrically, but for any one year the effect is strictly additive.
But part of me wonders if this is an elaborate snare you've set for us.
I would make the following argument in favor of 0.91% as being the answer to the right question.
Suppose an investment under management earns 20% per year, and suppose a manager charges an annual fee stated as being "10% of assets under management."
Then, at the start of the year, there is $1,000.
At the end of the year, before fees, there is $1,200.
The manager charges 10%.
The manager charges $120.
At the end of the year, after fees, there is $1,080.
Therefore, for purposes of calculating compound growth, the interest rate after fees is not 20% - 10% = 10%, it is 12%.
Where I definitely messed up was in using the word "shortfall" without explaining what I meant by it.
Last edited by nisiprius on Mon Feb 03, 2014 9:09 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.
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Re: Poll--especially for newbies--financial calc skills?
Unless you assume Ben bought a CD, which I did. Oops, I see the OP specified a fund.grabiner wrote: I believe the .908% is the correct answer because of the way compounding works. If you gain 5.307% and then lose 0.908%, your net gain is 4.351%. This is how you would report the numbers if you had the gain and loss in different time periods, so it makes just as much sense if you have the same gain and loss. And it also corresponds to how investments actually work; the expense ratio of your fund is charged on the current investment balance, not on the amount you had in the fund on the first day of the year.
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Re: Poll--especially for newbies--financial calc skills?
I called it a "fund" because that's the word John C. Bogle used. It wasn't a "mutual fund" organized under the investment company act of 1940, it was just a, well, a thingy, a trust, an account, a management dealy. Lawyers and bankers and clerks with, well I guess quill pens and ledgers. So you are still entitled to argue your point.frugaltype wrote:Unless you assume Ben bought a CD, which I did. Oops, I see the OP specified a fund.grabiner wrote: I believe the .908% is the correct answer because of the way compounding works. If you gain 5.307% and then lose 0.908%, your net gain is 4.351%. This is how you would report the numbers if you had the gain and loss in different time periods, so it makes just as much sense if you have the same gain and loss. And it also corresponds to how investments actually work; the expense ratio of your fund is charged on the current investment balance, not on the amount you had in the fund on the first day of the year.
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.
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Re: Poll--especially for newbies--financial calc skills?
Nisi and Grabiner have convinced me that .91% is correct.
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Re: Poll--especially for newbies--financial calc skills?
Perhaps I am being anal, but I wish there was a category for "I got approximately the same answer." Used a portable scientific calculator.
About the calculator; I teach computer science. About a month ago, I saw a scientific calculator in Big Lots for $2 that even did binary, octal, and hexadecimal calculations. Since my last small calculator that could do this was 30 years old, I bought it, and it worked well. Went into Dollar Tree Saturday and saw the same calculator for $1. I bought ten of them. I will loan them to my undergraduate students when they are taking my exams.
About the calculator; I teach computer science. About a month ago, I saw a scientific calculator in Big Lots for $2 that even did binary, octal, and hexadecimal calculations. Since my last small calculator that could do this was 30 years old, I bought it, and it worked well. Went into Dollar Tree Saturday and saw the same calculator for $1. I bought ten of them. I will loan them to my undergraduate students when they are taking my exams.
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Re: Poll--especially for newbies--financial calc skills?
I'd like to change the title of the thread but I'm scared that that will erase the poll results. I'd meant this to be an exploration of fairly basic and well-defined financial calculation skills. Instead, it has become a perfect exercise in how difficult it is to think clearly about such things, and how even a simple-seeming question can be ambiguous and have more than one "correct" answer.
I learned something today (sigh). I think I will go ahead and trot out the green emoticon because even though I am hugely reassured by Grabiner's agreement with me, I was arrogant in assuming I had the obviously correct answer to an obviously simple question.
I learned something today (sigh). I think I will go ahead and trot out the green emoticon because even though I am hugely reassured by Grabiner's agreement with me, I was arrogant in assuming I had the obviously correct answer to an obviously simple question.
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.
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Re: Poll--especially for newbies--financial calc skills?
Better yet, make them do the calcs by hand. WimpsDonCamillo wrote:Perhaps I am being anal, but I wish there was a category for "I got approximately the same answer." Used a portable scientific calculator.
About the calculator; I teach computer science. About a month ago, I saw a scientific calculator in Big Lots for $2 that even did binary, octal, and hexadecimal calculations. Since my last small calculator that could do this was 30 years old, I bought it, and it worked well. Went into Dollar Tree Saturday and saw the same calculator for $1. I bought ten of them. I will loan them to my undergraduate students when they are taking my exams.
Re: Poll--especially for newbies--financial calc skills?
Fees, like RMDs, are based on the balance at the beginning of the year. The $1000 grows to $1200 and $100 is taken out, leaving $1100, not $1080. No, that's not right either. The fee not only is based on the beginning of the year balance, it is taken out at the beginning of the year. $1000 becomes $900 which grows to $1080. Woah, where did that come from?nisiprius wrote:
Suppose an investment under management earns 20% per year, and suppose a manager charges an annual fee stated as being "10% of assets under management."
Then, at the start of the year, there is $1,000.
At the end of the year, before fees, there is $1,200.
The manager charges 10%.
The manager charges $120.
At the end of the year, after fees, there is $1,080.
Therefore, for purposes of calculating compound growth, the interest rate after fees is not 20% - 10% = 10%, it is 12%.
What you really need to know is the AAUM, which is what the fee is really based on, just as an ER is. The fee is $110. Is that taken out at the beginning or the end of the year?
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Re: Poll--especially for newbies--financial calc skills?
In the "good old days", hand calculators were prohibited in statistics exams. Unfair advantage to those with more $$ who could afford them.frugaltype wrote:Better yet, make them do the calcs by hand. WimpsDonCamillo wrote:Perhaps I am being anal, but I wish there was a category for "I got approximately the same answer." Used a portable scientific calculator.
About the calculator; I teach computer science. About a month ago, I saw a scientific calculator in Big Lots for $2 that even did binary, octal, and hexadecimal calculations. Since my last small calculator that could do this was 30 years old, I bought it, and it worked well. Went into Dollar Tree Saturday and saw the same calculator for $1. I bought ten of them. I will loan them to my undergraduate students when they are taking my exams.
Even once the prices dropped and calculators were on the course list along with textbooks, I required that students "show their work", so it was obvious they understood.
This also allowed us to deduct fewer points for a wrong answer if it was "just" an arithmetic mistake, and not a logical error from wrong setup or wrong measure being used, etc. Yes, much more time needed for "grading". But by the time computers - not calculators - were "doing everything", I cared much more that students understood what the statistics were really measuring, not whether they could feed raw data into a computer.
Nisiprius' question obviously would have given us some pause
RM
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Re: Poll--especially for newbies--financial calc skills?
Are you are just being pedantic, as in any finite number of digits is (usually) just an approximation? In my opinion, these here modren calculaytor gadgets should be good to a big ol' passel o' decimal places. So one should be able to get better than slide rule accuracy. In the original posting, I saidDonCamillo wrote:Perhaps I am being anal, but I wish there was a category for "I got approximately the same answer." Used a portable scientific calculator.
About the calculator; I teach computer science. About a month ago, I saw a scientific calculator in Big Lots for $2 that even did binary, octal, and hexadecimal calculations. Since my last small calculator that could do this was 30 years old, I bought it, and it worked well. Went into Dollar Tree Saturday and saw the same calculator for $1. I bought ten of them. I will loan them to my undergraduate students when they are taking my exams.
I believe the Dollar Tree calculator should have matched to that number of places, and if it didn't, it's a difference that needs a better explanation than "cheap calculator."nisiprius wrote:...a more precise calculation is 0.908126% per year.
Oddly enough, I too have six calculators that I bought for $3 apiece at Ocean State Job Lot and
5
÷
31
=
2ndF xth-root-of-y
200
=
+/-
+
1
=
x
100
=
is showing me
0.908126045
I mean this stuff is seriously amazing to anyone of my age. I don't know what's most amazing: that something that fits on a desk can actually extract a 200th root at all (I've heard rumors of Monroe/Friden-style rotary calculators capable of extracting a square root but never saw one in the flesh), or that you can buy that fits in a pocket for only $300 (HP-35), or that you can buy them for $3 each at Ocean State Job Lot. I don't think I want to know how just how many VAX-11/780s would be needed to match the calculating power of an iPhone.
Last edited by nisiprius on Mon Feb 03, 2014 9:57 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.
Re: Poll--especially for newbies--financial calc skills?
I got your answer to this problem.nisiprius wrote: "A certain investment A earns exactly the same percentage in interest every year for 200 years. If the investment trust had no fees, $1,000 would grow to $31,000,000 in 200 years. Every year, however, the managers take a fee of X% of the assets. If $1,000 actually grows to only $5,000,000 in 200 years, how large is X?"
This is not correct. 4.35/5.31 ~= 0.82nisiprius wrote: But, 4.350575848921% / 5.306895192401% = 0.99091873953996 = 99.091873953996%.
Last edited by rkhusky on Mon Feb 03, 2014 10:14 am, edited 2 times in total.
Re: Poll--especially for newbies--financial calc skills?
Okay, let me give another stab at this. I am trying to think of this in similar terms to the ER from a fund.
A) If you invest $1,000 for 200 years at a constant rate of 5.30690...% you'll end up with $31,000,000.
B) If you invest $1,000 for 200 years at a constant rate of 4.35058...% you'll end up with $5,000,000. But this does not matter anymore, at least in accordance with the way Nisi originally intended.
I set this up in Excel and went through 200 lines to see if it would come out to $5,000,000 and it did. I guess I took out the expense at the beginning of each year.
Year 1 came out to be (1,000-1,000*.90813...%)*(1+5.30690...%) = $1,043.51. Continuing down to year 200 gives me $5,000,000.00.
----------
To get .90813...% I solved for x using Excel as a calculator.:
5,000,000=1,000*((1+5.3069...%)*(1-x%))^200
A) If you invest $1,000 for 200 years at a constant rate of 5.30690...% you'll end up with $31,000,000.
B) If you invest $1,000 for 200 years at a constant rate of 4.35058...% you'll end up with $5,000,000. But this does not matter anymore, at least in accordance with the way Nisi originally intended.
C) Correct me if I'm wrong. This is the "alternate" way of looking at this problem, the way Nisi originally intended. The new wording makes the problem a lot more clear to me. The investment will still earn 5.30690...% per year but a portion of the investment will be subtracted, sort of like Expense Ratio. The portion that is subtracted every single year is .90813...% of assets.nisiprius wrote:"A certain investment A earns exactly the same percentage in interest every year for 200 years. If the investment trust had no fees, $1,000 would grow to $31,000,000 in 200 years. Every year, however, the managers take a fee of X% of the assets. If $1,000 actually grows to only $5,000,000 in 200 years, how large is X?"
I set this up in Excel and went through 200 lines to see if it would come out to $5,000,000 and it did. I guess I took out the expense at the beginning of each year.
Year 1 came out to be (1,000-1,000*.90813...%)*(1+5.30690...%) = $1,043.51. Continuing down to year 200 gives me $5,000,000.00.
----------
To get .90813...% I solved for x using Excel as a calculator.:
5,000,000=1,000*((1+5.3069...%)*(1-x%))^200
Last edited by red5 on Mon Feb 03, 2014 10:36 am, edited 1 time in total.
Re: Poll--especially for newbies--financial calc skills?
When I learned how to do compound interest pocket calculators didn't exist. It was strictly log tables. We did eventually have a field trip to a DEC plant in Maynard Mass where they had a lab with some Wang calculators complete with Nixie tubes. It was geek heaven.ResearchMed wrote:In the "good old days", hand calculators were prohibited in statistics exams. Unfair advantage to those with more $$ who could afford them.frugaltype wrote:Better yet, make them do the calcs by hand. WimpsDonCamillo wrote:Perhaps I am being anal, but I wish there was a category for "I got approximately the same answer." Used a portable scientific calculator.
About the calculator; I teach computer science. About a month ago, I saw a scientific calculator in Big Lots for $2 that even did binary, octal, and hexadecimal calculations. Since my last small calculator that could do this was 30 years old, I bought it, and it worked well. Went into Dollar Tree Saturday and saw the same calculator for $1. I bought ten of them. I will loan them to my undergraduate students when they are taking my exams.
RM
In honor of this question I got out my book of log tables.
Re: Poll--especially for newbies--financial calc skills?
This is a test to see if we know how fees are applied.
Starting with the formula for an amount at compound interest
A = P * (1+I)^T
are fees applied like this
A = P * (1 + (I-F))^T
or like this
A = P * ( (1+I)*(1-F) )^T
Ron
Starting with the formula for an amount at compound interest
A = P * (1+I)^T
are fees applied like this
A = P * (1 + (I-F))^T
or like this
A = P * ( (1+I)*(1-F) )^T
Ron
Money is fungible |
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- swimirvine
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Re: Poll--especially for newbies--financial calc skills?
31,000,000/1000 = 31,000
The 200th root of 31,000 = 1.053068952
or
5.3068952%
5,000,000/1000 = 5,000
The 200th root of 5,000 = 1.043505758
or
4.3505758%
5.3068952% - 4.3505758% = 0.9563194%
on a hand calculator it was just one step - I just entered 31000 "x-root-y" 200
The 200th root of 31,000 = 1.053068952
or
5.3068952%
5,000,000/1000 = 5,000
The 200th root of 5,000 = 1.043505758
or
4.3505758%
5.3068952% - 4.3505758% = 0.9563194%
on a hand calculator it was just one step - I just entered 31000 "x-root-y" 200
The way I invest my money is not the right way to invest, it's the right way for ME to invest.
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Re: Poll--especially for newbies--financial calc skills?
As a student in 1970, I was a research assistant for a defense contractor trying to determine pilot's preference for the optimal layout of instruments in Navy jet fighter aircraft. I spent an entire semester, fifteen hours per week, performing one matrix multiplication on a Friden mechanical calculator. I think it multiplied a 5 by 10 (or 15) matrix by a 5 by 50 matrix. Each 14 step mechanical operation had to be done 3 times to be sure I got the right result, and there were thousands of them. Ten years later, when I learned to program in APL, I could have done the whole problem, including data entry, three times in half an hour.nisiprius wrote: I mean this stuff is seriously amazing to anyone of my age. I don't know what's most amazing: that something that fits on a desk can actually extract a 200th root at all (I've heard rumors of Monroe/Friden-style rotary calculators capable of extracting a square root but never saw one in the flesh), or that you can buy that fits in a pocket for only $300 (HP-35), or that you can buy them for $3 each at Ocean State Job Lot. I don't think I want to know how just how many VAX-11/780s would be needed to match the calculating power of an iPhone.
Incidentally, my calculator answer to the problem was only different because I did a quick and dirty approximation to verify the numbers instead of taking the time to do the problem. (30 seconds vs two minutes?) I was once the CFO for a privately held publishing company. Doing mental arithmetic, I would sometimes make order of magnitude errors in discussing financials with my boss, the owner. He was not formally educated in finance, but it was his money. He caught those errors immediately. I got into the habit of quick and dirty calculator approximations because I could do that during a conversation with him.
The order of magnitude errors probably were the result of my earlier use of a slide rule, where it is easy to get the numbers, but you had to do the magnitude in your head. I learned the slide rule from the guy sitting next to me in 11th grade chemistry class in 1961. It was fun to get an answer to a question the teacher asked in thirty seconds, when no one except the two of us could do it in two minutes, and those who had to use simple algebra took five minutes.
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- jimb_fromATL
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Re: Poll--especially for newbies--financial calc skills?
Agreed. All the others who that came up with the difference in average APY are correct about the average APY, but are overlooking that the expenses are on the total assets, not just the interest earned every year. So the actual expense ratio is not as much as the difference in rate.C) Correct me if I'm wrong. This is the "alternate" way of looking at this problem, the way Nisi originally intended. The new wording makes the problem a lot more clear to me. The investment will still earn 5.30690...% per year but a portion of the investment will be subtracted, sort of like Expense Ratio. The portion that is subtracted every single year is .90813...% of assets.
I set this up in Excel and went through 200 lines to see if it would come out to $5,000,000 and it did. I guess I took out the expense at the beginning of each year.
Year 1 came out to be (1,000-1,000*.90813...%)*(1+5.30690...%) = $1,043.51. Continuing down to year 200 gives me $5,000,000.00.
jimb
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Re: Poll--especially for newbies--financial calc skills?
I meant 104.350575848921% / 105.306895192401% = 0.99091873953996 = 99.091873953996%.rkhusky wrote:I got your answer to this problem.nisiprius wrote: "A certain investment A earns exactly the same percentage in interest every year for 200 years. If the investment trust had no fees, $1,000 would grow to $31,000,000 in 200 years. Every year, however, the managers take a fee of X% of the assets. If $1,000 actually grows to only $5,000,000 in 200 years, how large is X?"
This is not correct. 4.35/5.31 ~= 0.82nisiprius wrote: But, 4.350575848921% / 5.306895192401% = 0.99091873953996 = 99.091873953996%.
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.
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Re: Poll--especially for newbies--financial calc skills?
Uh, is that your final answer?nisiprius wrote:I meant 104.350575848921% / 105.306895192401% = 0.99091873953996 = 99.091873953996%.rkhusky wrote:I got your answer to this problem.nisiprius wrote: "A certain investment A earns exactly the same percentage in interest every year for 200 years. If the investment trust had no fees, $1,000 would grow to $31,000,000 in 200 years. Every year, however, the managers take a fee of X% of the assets. If $1,000 actually grows to only $5,000,000 in 200 years, how large is X?"
This is not correct. 4.35/5.31 ~= 0.82nisiprius wrote: But, 4.350575848921% / 5.306895192401% = 0.99091873953996 = 99.091873953996%.
RM
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Re: Poll--especially for newbies--financial calc skills?
The way this thread is going (or the way my brain is going... going... gone!) probably not. But, I am learning a lot. "The best way to learn something on the Internet is not to ask a question, but to post inaccurate information."ResearchMed wrote:Uh, is that your final answer?I meant 104.350575848921% / 105.306895192401% = 0.99091873953996 = 99.091873953996%.
RM
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.
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Re: Poll--especially for newbies--financial calc skills?
Love this!nisiprius wrote:
... "The best way to learn something on the Internet is not to ask a question, but to post inaccurate information."
Hadn't heard it before. (Gotta get out more?)
RM
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Re: Poll--especially for newbies--financial calc skills?
I probably count as a newbie. As a contrast to all the precise answers, here is the way I would roughly calculate it:
$1000 growing to $5,000,000.
I enter 1000 on my non-financial pocket calculator, punch x2, and then push "=" multiple times, and see how many "doubles" it takes to get it close to 5 million. The answer I got is 12 doubles. Therefore, 200 years divided by 12 says the doubling occurred once every 16 years. Using the rule of 72, this means the interest rate was 72/16 = 4.5%
$1000 growing to $31,000,000.
Continuing, I then push "=" more times, and see how many "doubles" it takes to get it close to 31 million. The answer I got is 16 doubles. Therefore, 200 years divided by 16 says the doubling occurred once every 13 years. Using the rule of 72, this means the interest rate was 72/13 = 5.5%
So the annual difference I get with this very crude estimate is 1%. Close enough for me to conclude that I believe your answer (either one).
$1000 growing to $5,000,000.
I enter 1000 on my non-financial pocket calculator, punch x2, and then push "=" multiple times, and see how many "doubles" it takes to get it close to 5 million. The answer I got is 12 doubles. Therefore, 200 years divided by 12 says the doubling occurred once every 16 years. Using the rule of 72, this means the interest rate was 72/16 = 4.5%
$1000 growing to $31,000,000.
Continuing, I then push "=" more times, and see how many "doubles" it takes to get it close to 31 million. The answer I got is 16 doubles. Therefore, 200 years divided by 16 says the doubling occurred once every 13 years. Using the rule of 72, this means the interest rate was 72/13 = 5.5%
So the annual difference I get with this very crude estimate is 1%. Close enough for me to conclude that I believe your answer (either one).
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Re: Poll--especially for newbies--financial calc skills?
If you are planning to compute the effect of expenses, one should keep in mind that published ERs are forward-looking guesses. And if you look in your fund's annual report, you'll see another kind of expense ratio. In this ratio, the numerator is the total dollar amount subtracted from the funds assets due to expenses, and the denominator is (I believe) the average daily AUM for the year in question.
Somewhat tangential to this thread, but it does suggest that working out the effects of costs to 6 decimal places is an exercise in false precision.
Somewhat tangential to this thread, but it does suggest that working out the effects of costs to 6 decimal places is an exercise in false precision.
Re: Poll--especially for newbies--financial calc skills?
Yes, exactly! I answered 0.95% to start with (using something akin to your 2nd formula), and then pondered how the heck could anybody come up with 0.91%. Then thought that maybe fees are charged at the beginning of the year. And I used something akin to your 3rd formula, and did find 0.91%. And then parsed the thread and found your post!Oicuryy wrote:This is a test to see if we know how fees are applied.
Starting with the formula for an amount at compound interest
A = P * (1+I)^T
are fees applied like this
A = P * (1 + (I-F))^T
or like this
A = P * ( (1+I)*(1-F) )^T
Ron
But then I realized this has nothing to do with the timing of the fees, as A = P * ( (1+I)*(1-F) )^T is the same as A = P * ( (1-F)*(1+I) )^T. Plus fees are probably charged on a monthly basis anyway.
And yes, thinking twice about it, the 3rd formula makes more sense than the 2nd one. Could it be that Nisiprius was right after all! Apologies on behalf of one of the few guys who voted that you messed up...
PS. now this makes me wonder how Firecalc, cFIREsim and the likes do the math!
- jimb_fromATL
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Re: Poll--especially for newbies--financial calc skills?
For that matter, so is looking at the growth of a lump sum --like the usual $10K-- over X number of years based on published yearly returns when deciding where to invest for retirement. I don't know a single soul who ever invested a single lump sum at exactly the beginning of a year and never put in any more or took anything out for 30 or 40 years before retirement.House Blend wrote:
Somewhat tangential to this thread, but it does suggest that working out the effects of costs to 6 decimal places is an exercise in false precision.
For periodic contributions like monthly for a 401(k) or even yearly for an IRA -- which are both Dollar-Cost-Averaging--the compound average growth rate can be substantially different ... especially during the wild rides up and down in 2001 and 2008.
jimb
Re: Poll--especially for newbies--financial calc skills?
siamond wrote:Yes, exactly! I answered 0.95% to start with (using something akin to your 2nd formula), and then pondered how the heck could anybody come up with 0.91%. Then thought that maybe fees are charged at the beginning of the year. And I used something akin to your 3rd formula, and did find 0.91%. And then parsed the thread and found your post!
But then I realized this has nothing to do with the timing of the fees, as A = P * ( (1+I)*(1-F) )^T is the same as A = P * ( (1-F)*(1+I) )^T. Plus fees are probably charged on a monthly basis anyway.
And yes, thinking twice about it, the 3rd formula makes more sense than the 2nd one. Could it be that Nisiprius was right after all! Apologies on behalf of one of the few guys who voted that you messed up...
PS. now this makes me wonder how Firecalc, cFIREsim and the likes do the math!
Or to anyone else, it should still be fair to say that he did in fact make .95% less per year because of this .91% fee that was taken every year for a management fee, correct? I, along with a few other people, misinterpreted what Nisiprius was actually asking for in the first place.nisiprius wrote:"A certain investment A earns exactly the same percentage in interest every year for 200 years. If the investment trust had no fees, $1,000 would grow to $31,000,000 in 200 years. Every year, however, the managers take a fee of X% of the assets. If $1,000 actually grows to only $5,000,000 in 200 years, how large is X?"
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Re: Poll--especially for newbies--financial calc skills?
My trusty old HP-12C (financial calculator) got me to .9563%. That calculator has been going since about 1990. I have only changed the batteries once, or maybe twice.
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Re: Poll--especially for newbies--financial calc skills?
Excel solver is quick. 0.956%.
On the other hand, wordsmithing gets me to the other answer.
RM
On the other hand, wordsmithing gets me to the other answer.
RM
I figure the odds be fifty-fifty I just might have something to say. FZ
Re: Poll--especially for newbies--financial calc skills?
I used an inexpensive TI-30Xa Scientific Calculator.
31000 to the .005 power = 1.053068952 or 5.3068952%
5000 to the .005 power = 1.043505758 or 4.3505758%
The difference in percentages is 0.9563193%.
31000 to the .005 power = 1.053068952 or 5.3068952%
5000 to the .005 power = 1.043505758 or 4.3505758%
The difference in percentages is 0.9563193%.
Enjoying the Outdoors
- jimb_fromATL
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Re: Poll--especially for newbies--financial calc skills?
Yep, that's the difference in the net average percentage rate per year. But the expense percentage is smaller because expenses are on the whole balance, not just the interest earned each year.Electron wrote:I used an inexpensive TI-30Xa Scientific Calculator.
31000 to the .005 power = 1.053068952 or 5.3068952%
5000 to the .005 power = 1.043505758 or 4.3505758%
The difference in percentages is 0.9563193%.
jimb
Re: Poll--especially for newbies--financial calc skills?
It reminds me of this: http://xkcd.com/386/ResearchMed wrote:Love this!nisiprius wrote:
... "The best way to learn something on the Internet is not to ask a question, but to post inaccurate information."
Hadn't heard it before. (Gotta get out more?)
RM
"Yes, investing is simple. But it is not easy, for it requires discipline, patience, steadfastness, and that most uncommon of all gifts, common sense." ~Jack Bogle
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Re: Poll--especially for newbies--financial calc skills?
Good one, perfectFallible wrote:It reminds me of this: http://xkcd.com/386/ResearchMed wrote:Love this!nisiprius wrote:
... "The best way to learn something on the Internet is not to ask a question, but to post inaccurate information."
Hadn't heard it before. (Gotta get out more?)
RM
Thanks!
RM