Is the effective interest rate of a loan higher when it’s early in amortization period?

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Clarice
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Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Wed Nov 06, 2019 1:19 pm

All else equal, paying down a loan with 5% interest is a wiser decision than paying down a loan with 4% interest - understood.

What if the 4% loan is very early in amort period vs. 5% loan is almost all principal - you could be saving more in interest dollars paid, no?

Same question goes for if both rates are the same - what if one loan is amortizing and one loan is a term loan?

And I’ve been working in financial services for 5 years! :oops:

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JoeRetire
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by JoeRetire » Wed Nov 06, 2019 1:24 pm

The rate is the rate. It doesn't change due to how far into the amortization period you are.

alex_686
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by alex_686 » Wed Nov 06, 2019 1:27 pm

Clarice wrote:
Wed Nov 06, 2019 1:19 pm
Same question goes for if both rates are the same - what if one loan is amortizing and one loan is a term loan?
If you pay down a 4% loan you are paying down at a effective rate of 4%. It does not matter if it is day 1 or the 29th year of a 30 year mortgage. Same for 5%.

The correct answer is pretty easy and intuitive if you think about it. First, treat the loan as a negative bond. Figure out what your correct asset allocation is. Figure out how you want to invest your additional dollars. Think about the loan in terms of opportunity costs. Think about the (mostly modest) impact of leverage, cash flow requirements (i.e. flexibility), and your risk adjusted return.

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dm200
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by dm200 » Wed Nov 06, 2019 1:28 pm

Clarice wrote:
Wed Nov 06, 2019 1:19 pm
All else equal, paying down a loan with 5% interest is a wiser decision than paying down a loan with 4% interest - understood.
What if the 4% loan is very early in amort period vs. 5% loan is almost all principal - you could be saving more in interest dollars paid, no?
Same question goes for if both rates are the same - what if one loan is amortizing and one loan is a term loan?
And I’ve been working in financial services for 5 years! :oops:
No, assuming interest on both loans is calculated on the daily outstanding balance. Is interest on the term loan calculated on the daily outstanding balance?

The interest rate is the interest rate.

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Clarice
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Wed Nov 06, 2019 1:31 pm

If I have two loans with the same interest rate starting at exactly the same time, the amortizing loan has more interest dollars up front - so i would be better off paying that loan first.... no?

alex_686
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by alex_686 » Wed Nov 06, 2019 1:44 pm

Clarice wrote:
Wed Nov 06, 2019 1:31 pm
If I have two loans with the same interest rate starting at exactly the same time, the amortizing loan has more interest dollars up front - so i would be better off paying that loan first.... no?
No.

You need to compare apples to apples. This means you must keep the cash flows the same under both analysis.

Let us say you have 2 loans and a extra $X to pay down one loan. Once you pay off one loan, you will direct the cash flow servicing that loan to pay off the other. Now, which loan should you pay off first? It does not matter. You will have the same end date both ways. You will pay the same interest either way. Note, this assumes identical cash flows and interest rates.

I think I know what you are thinking. It is like the idea that heavy objects fall faster than light ones. Intuitive but wrong.

nehawk87
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by nehawk87 » Wed Nov 06, 2019 1:47 pm

Doesn’t matter. The only thing changing as a loan amortizes is the amount of the loan balance subject to interest.

Monster99
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Monster99 » Wed Nov 06, 2019 1:54 pm

The rate is the rate - if you pay down the principal the duration changes and the total amount of interest paid is less but the rate is the same.

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Clarice
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Wed Nov 06, 2019 2:07 pm

Sorry all let me rephrase the question in the title then -

Is it a better decision to pay off one loan vs. another when everything about those two loans is the same ASIDE from the fact that one loan is term and one loan is amortizing, and we are early in amort period?

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Clarice
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Amortizing v. term loan, same rates, early in amort period - what to pay off first?

Post by Clarice » Wed Nov 06, 2019 2:08 pm

Clarice wrote:
Wed Nov 06, 2019 1:19 pm
All else equal, paying down a loan with 5% interest is a wiser decision than paying down a loan with 4% interest - understood.

What if the 4% loan is very early in amort period vs. 5% loan is almost all principal - you could be saving more in interest dollars paid, no?

Same question goes for if both rates are the same - what if one loan is amortizing and one loan is a term loan?

And I’ve been working in financial services for 5 years! :oops:

alex_686
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by alex_686 » Wed Nov 06, 2019 2:14 pm

Clarice wrote:
Wed Nov 06, 2019 2:07 pm
Is it a better decision to pay off one loan vs. another when everything about those two loans is the same ASIDE from the fact that one loan is term and one loan is amortizing, and we are early in amort period?
Sorry, the answer is still "no" - there is no difference. The math is ironclad on this. No way to get around this. We could look at second order factors.

I might favor paying off the shorter term loan first. You would pay that one off first, giving one the optionality of paying down the longer dated loan next (see my cash flow analysis up top) or of redirecting that cash flow to some other endeavor - either as another investment or having extra flexibility to handle emergencies.

On the other hand, I might favor paying off the longer term loan - for exactly the same reason. Some people find it had to maintain discipline when investing. It is so much easier to skip a payment towards your IRA and buy that expensive toy / vacation / extra weekly latte. No optionality, so you are forced to "save" by "investing" in your negative bond.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Wed Nov 06, 2019 2:16 pm

I do not agree. If I have a limited amount of money to prepay one loan or the other then I save more interest dollars today by paying towards the amortizing loan...

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by CedarWaxWing » Wed Nov 06, 2019 2:22 pm

Clarice wrote:
Wed Nov 06, 2019 2:16 pm
I do not agree. If I have a limited amount of money to prepay one loan or the other then I save more interest dollars today by paying towards the amortizing loan...
Please show your math in regards to how you come to this conclusion.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by magicrat » Wed Nov 06, 2019 2:27 pm

Clarice wrote:
Wed Nov 06, 2019 2:07 pm
one loan is term and one loan is amortizing
What does this even mean? Please define what you mean by a "term" loan and an "amortizing" loan.

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Clarice
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Wed Nov 06, 2019 2:32 pm

CedarWaxWing wrote:
Wed Nov 06, 2019 2:22 pm
Clarice wrote:
Wed Nov 06, 2019 2:16 pm
I do not agree. If I have a limited amount of money to prepay one loan or the other then I save more interest dollars today by paying towards the amortizing loan...
Please show your math in regards to how you come to this conclusion.
Will follow up.

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Clarice
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Wed Nov 06, 2019 2:32 pm

magicrat wrote:
Wed Nov 06, 2019 2:27 pm
Clarice wrote:
Wed Nov 06, 2019 2:07 pm
one loan is term and one loan is amortizing
What does this even mean? Please define what you mean by a "term" loan and an "amortizing" loan.
Term loans do not amortize.

magicrat
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by magicrat » Wed Nov 06, 2019 2:38 pm

Clarice wrote:
Wed Nov 06, 2019 2:32 pm
magicrat wrote:
Wed Nov 06, 2019 2:27 pm
Clarice wrote:
Wed Nov 06, 2019 2:07 pm
one loan is term and one loan is amortizing
What does this even mean? Please define what you mean by a "term" loan and an "amortizing" loan.
Term loans do not amortize.
That is not a definition. I'm not sure that you understand how loans work. Again, please define what you mean by these two types of loans. Better yet, provide a mathematical example for each.

alex_686
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by alex_686 » Wed Nov 06, 2019 2:46 pm

Clarice wrote:
Wed Nov 06, 2019 2:32 pm
Term loans do not amortize.
Are you thinking about a revolving line of credit which has no fixed end date? Much like a credit card?

If so - the answer is still no. The math still holds. After all, one only needs an interest rate and a cash flow. Interest paid will remain the same.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Wed Nov 06, 2019 2:49 pm

magicrat wrote:
Wed Nov 06, 2019 2:38 pm
Clarice wrote:
Wed Nov 06, 2019 2:32 pm
magicrat wrote:
Wed Nov 06, 2019 2:27 pm
Clarice wrote:
Wed Nov 06, 2019 2:07 pm
one loan is term and one loan is amortizing
What does this even mean? Please define what you mean by a "term" loan and an "amortizing" loan.
Term loans do not amortize.
That is not a definition. I'm not sure that you understand how loans work. Again, please define what you mean by these two types of loans. Better yet, provide a mathematical example for each.
Because you don’t understand you tell me that I must not understand myself?

Term loan = fixed P&I per payment (think personal loans I believe)
Amortizing loan = front-loaded with interest (think mortgage)

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ResearchMed
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by ResearchMed » Wed Nov 06, 2019 2:52 pm

Clarice wrote:
Wed Nov 06, 2019 2:32 pm
magicrat wrote:
Wed Nov 06, 2019 2:27 pm
Clarice wrote:
Wed Nov 06, 2019 2:07 pm
one loan is term and one loan is amortizing
What does this even mean? Please define what you mean by a "term" loan and an "amortizing" loan.
Term loans do not amortize.
How is this "term loan" repaid, if paying the 'minimum due". to make an appropriate comparison with the amortizing loan?

RM
This signature is a placebo. You are in the control group.

alex_686
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by alex_686 » Wed Nov 06, 2019 3:05 pm

Clarice wrote:
Wed Nov 06, 2019 2:49 pm
Term loan = fixed P&I per payment (think personal loans I believe)
If P&I is fixed, than you can't make early payments so this question is more or less moot.

May I ask where you live? I somebody who has worked in banking compliance this is externally rare in the US for personal loans. It has been a few years, but I think the sole exception might be early payment penalties on a few products. This makes the math a bit more interesting but it is not going to shift the analysis much.

Once again, the only inputs you need to know in this situation is interest rate and cash flow. The rest can flow from that.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by ray.james » Wed Nov 06, 2019 3:59 pm

Are you talking about term loan with variable payments. These do occur in other countries but no USA.

Personal, 401k, auto, mortgage are all amortized loans in USA. Some pay day loans look like term loan but even they amortize since the unpaid is rolled over to next loan.

IN Brazil/India/China there are term loans tied to some thing like banks individual prime rate that adjusts every quarter/year. This changes payment. Somewhat equivalent is ARM loans for mortgage in USA.

Even then, math is math. Pay off the higher interest rate unless there is expected term adjustment that is going to increase it substantially. Then you can adjust the interest rate on that loan to some equivalent number for apples to apples comparison.

BTW: I think you have it opposite. Here is the definition of amortize
::to pay off (an obligation, such as a mortgage) gradually usually by periodic payments of principal and interest or by payments to a sinking fund
When in doubt, http://www.bogleheads.org/forum/viewtopic.php?f=1&t=79939

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Wed Nov 06, 2019 4:52 pm

Thanks for the help, all. Probably could have been a little clearer in the product type I was referencing. Better off paying amortizing loan before a fixed principal loan it looks like.

To the poster who said fixed-principal products don't exist in the US - I doubt that as it is more beneficial for the consumer.

Code: Select all

AMORTIZING				
Rate	5%			
Term (months)	 60 			
				
Period	Balance	Principal	Interest	Payment
0 	$1,000,000 			
1 	$985,295 	$14,705 	$4,167 	$18,871 
2 	$970,530 	$14,766 	$4,105 	$18,871 
3 	$955,702 	$14,827 	$4,044 	$18,871 
4 	$940,813 	$14,889 	$3,982 	$18,871 
5 	$925,862 	$14,951 	$3,920 	$18,871 
6 	$910,848 	$15,013 	$3,858 	$18,871 
7 	$895,772 	$15,076 	$3,795 	$18,871 
8 	$880,634 	$15,139 	$3,732 	$18,871 
9 	$865,432 	$15,202 	$3,669 	$18,871 
10 	$850,166 	$15,265 	$3,606 	$18,871 
11 	$834,837 	$15,329 	$3,542 	$18,871 
12 	$819,445 	$15,393 	$3,478 	$18,871 
13 	$803,988 	$15,457 	$3,414 	$18,871 
14 	$788,467 	$15,521 	$3,350 	$18,871 
15 	$772,881 	$15,586 	$3,285 	$18,871 
16 	$757,230 	$15,651 	$3,220 	$18,871 
17 	$741,514 	$15,716 	$3,155 	$18,871 
18 	$725,732 	$15,782 	$3,090 	$18,871 
19 	$709,885 	$15,847 	$3,024 	$18,871 
20 	$693,971 	$15,913 	$2,958 	$18,871 
21 	$677,992 	$15,980 	$2,892 	$18,871 
22 	$661,945 	$16,046 	$2,825 	$18,871 
23 	$645,832 	$16,113 	$2,758 	$18,871 
24 	$629,652 	$16,180 	$2,691 	$18,871 
25 	$613,404 	$16,248 	$2,624 	$18,871 
26 	$597,089 	$16,315 	$2,556 	$18,871 
27 	$580,706 	$16,383 	$2,488 	$18,871 
28 	$564,254 	$16,452 	$2,420 	$18,871 
29 	$547,734 	$16,520 	$2,351 	$18,871 
30 	$531,145 	$16,589 	$2,282 	$18,871 
31 	$514,487 	$16,658 	$2,213 	$18,871 
32 	$497,759 	$16,728 	$2,144 	$18,871 
33 	$480,962 	$16,797 	$2,074 	$18,871 
34 	$464,095 	$16,867 	$2,004 	$18,871 
35 	$447,157 	$16,938 	$1,934 	$18,871 
36 	$430,149 	$17,008 	$1,863 	$18,871 
37 	$413,070 	$17,079 	$1,792 	$18,871 
38 	$395,920 	$17,150 	$1,721 	$18,871 
39 	$378,698 	$17,222 	$1,650 	$18,871 
40 	$361,405 	$17,293 	$1,578 	$18,871 
41 	$344,040 	$17,365 	$1,506 	$18,871 
42 	$326,602 	$17,438 	$1,433 	$18,871 
43 	$309,092 	$17,510 	$1,361 	$18,871 
44 	$291,508 	$17,583 	$1,288 	$18,871 
45 	$273,852 	$17,657 	$1,215 	$18,871 
46 	$256,121 	$17,730 	$1,141 	$18,871 
47 	$238,317 	$17,804 	$1,067 	$18,871 
48 	$220,439 	$17,878 	$993 	$18,871 
49 	$202,486 	$17,953 	$918 	$18,871 
50 	$184,459 	$18,028 	$844 	$18,871 
51 	$166,356 	$18,103 	$769 	$18,871 
52 	$148,178 	$18,178 	$693 	$18,871 
53 	$129,924 	$18,254 	$617 	$18,871 
54 	$111,594 	$18,330 	$541 	$18,871 
55 	$93,188 	$18,406 	$465 	$18,871 
56 	$74,705 	$18,483 	$388 	$18,871 
57 	$56,145 	$18,560 	$311 	$18,871 
58 	$37,508 	$18,637 	$234 	$18,871 
59 	$18,793 	$18,715 	$156 	$18,871 
60 	$0 	$18,793 	$78 	$18,871 
Total			$132,274 	$1,132,274 

Code: Select all

FIXED PRINCIPAL				
Rate	5%			
Term (months)	 60 			
				
Period	Balance	Principal	Interest	Payment
0 	$1,000,000 			
1 	$983,333 	$16,667 	$4,167 	$20,833 
2 	$966,667 	$16,667 	$4,097 	$20,764 
3 	$950,000 	$16,667 	$4,028 	$20,694 
4 	$933,333 	$16,667 	$3,958 	$20,625 
5 	$916,667 	$16,667 	$3,889 	$20,556 
6 	$900,000 	$16,667 	$3,819 	$20,486 
7 	$883,333 	$16,667 	$3,750 	$20,417 
8 	$866,667 	$16,667 	$3,681 	$20,347 
9 	$850,000 	$16,667 	$3,611 	$20,278 
10 	$833,333 	$16,667 	$3,542 	$20,208 
11 	$816,667 	$16,667 	$3,472 	$20,139 
12 	$800,000 	$16,667 	$3,403 	$20,069 
13 	$783,333 	$16,667 	$3,333 	$20,000 
14 	$766,667 	$16,667 	$3,264 	$19,931 
15 	$750,000 	$16,667 	$3,194 	$19,861 
16 	$733,333 	$16,667 	$3,125 	$19,792 
17 	$716,667 	$16,667 	$3,056 	$19,722 
18 	$700,000 	$16,667 	$2,986 	$19,653 
19 	$683,333 	$16,667 	$2,917 	$19,583 
20 	$666,667 	$16,667 	$2,847 	$19,514 
21 	$650,000 	$16,667 	$2,778 	$19,444 
22 	$633,333 	$16,667 	$2,708 	$19,375 
23 	$616,667 	$16,667 	$2,639 	$19,306 
24 	$600,000 	$16,667 	$2,569 	$19,236 
25 	$583,333 	$16,667 	$2,500 	$19,167 
26 	$566,667 	$16,667 	$2,431 	$19,097 
27 	$550,000 	$16,667 	$2,361 	$19,028 
28 	$533,333 	$16,667 	$2,292 	$18,958 
29 	$516,667 	$16,667 	$2,222 	$18,889 
30 	$500,000 	$16,667 	$2,153 	$18,819 
31 	$483,333 	$16,667 	$2,083 	$18,750 
32 	$466,667 	$16,667 	$2,014 	$18,681 
33 	$450,000 	$16,667 	$1,944 	$18,611 
34 	$433,333 	$16,667 	$1,875 	$18,542 
35 	$416,667 	$16,667 	$1,806 	$18,472 
36 	$400,000 	$16,667 	$1,736 	$18,403 
37 	$383,333 	$16,667 	$1,667 	$18,333 
38 	$366,667 	$16,667 	$1,597 	$18,264 
39 	$350,000 	$16,667 	$1,528 	$18,194 
40 	$333,333 	$16,667 	$1,458 	$18,125 
41 	$316,667 	$16,667 	$1,389 	$18,056 
42 	$300,000 	$16,667 	$1,319 	$17,986 
43 	$283,333 	$16,667 	$1,250 	$17,917 
44 	$266,667 	$16,667 	$1,181 	$17,847 
45 	$250,000 	$16,667 	$1,111 	$17,778 
46 	$233,333 	$16,667 	$1,042 	$17,708 
47 	$216,667 	$16,667 	$972 	$17,639 
48 	$200,000 	$16,667 	$903 	$17,569 
49 	$183,333 	$16,667 	$833 	$17,500 
50 	$166,667 	$16,667 	$764 	$17,431 
51 	$150,000 	$16,667 	$694 	$17,361 
52 	$133,333 	$16,667 	$625 	$17,292 
53 	$116,667 	$16,667 	$556 	$17,222 
54 	$100,000 	$16,667 	$486 	$17,153 
55 	$83,333 	$16,667 	$417 	$17,083 
56 	$66,667 	$16,667 	$347 	$17,014 
57 	$50,000 	$16,667 	$278 	$16,944 
58 	$33,333 	$16,667 	$208 	$16,875 
59 	$16,667 	$16,667 	$139 	$16,806 
60 	$0 	$16,667 	$69 	$16,736 
Total			$127,083 	$1,127,083 

chevca
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by chevca » Wed Nov 06, 2019 5:01 pm

Clarice wrote:
Wed Nov 06, 2019 2:49 pm
magicrat wrote:
Wed Nov 06, 2019 2:38 pm
Clarice wrote:
Wed Nov 06, 2019 2:32 pm
magicrat wrote:
Wed Nov 06, 2019 2:27 pm
Clarice wrote:
Wed Nov 06, 2019 2:07 pm
one loan is term and one loan is amortizing
What does this even mean? Please define what you mean by a "term" loan and an "amortizing" loan.
Term loans do not amortize.
That is not a definition. I'm not sure that you understand how loans work. Again, please define what you mean by these two types of loans. Better yet, provide a mathematical example for each.
Because you don’t understand you tell me that I must not understand myself?

Term loan = fixed P&I per payment (think personal loans I believe)
Amortizing loan = front-loaded with interest (think mortgage)
I think you believe wrong.

Unless you're talking a different personal loan than most of us are familiar with, it's basically the same as a mortgage. Whatever amount you borrowed, you can pay it off the next month and never pay interest on it again.

Technically a mortgage could be considered a fixed P&I per payment. If you check the amortization table given to you at closing time, it will tell what you will pay for P&I for 30 years. But, you can pay it down aggressively and effectively jump ahead on the schedule/table. Same as with a car loan or a personal loan. You will get a fixed payment amount on all of them. But, the monthly P&I amounts are figured off the remaining balance.

Mortgages are not "front loaded" with interest. You pay more interest in the early monthly payments simply because that's when the balance is bigger. When the balance gets lower, you pay less of the payment in interest.... same on a car or personal loan.

There is no effective rate (outside tax stuff) on a loan. The rate is the rate... same in month 1 as in month 30.

The true part of what I've read from you is, the sooner you pay extra on a loan... the more, the sooner, the better... the less total interest you pay on that loan. But, it has nothing to do with effective rates, or front loaded, or anything like that. It's simply because you lower the balance that much sooner. Or, you throw an extra $10k at a loan in month 2 (for example), you never pay interest on that $10k again.

chevca
Posts: 2792
Joined: Wed Jul 26, 2017 11:22 am

Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by chevca » Wed Nov 06, 2019 5:06 pm

Clarice wrote:
Wed Nov 06, 2019 4:52 pm
Thanks for the help, all. Probably could have been a little clearer in the product type I was referencing. Better off paying amortizing loan before a fixed principal loan it looks like.

To the poster who said fixed-principal products don't exist in the US - I doubt that as it is more beneficial for the consumer.

Code: Select all

AMORTIZING				
Rate	5%			
Term (months)	 60 			
				
Period	Balance	Principal	Interest	Payment
0 	$1,000,000 			
1 	$985,295 	$14,705 	$4,167 	$18,871 
2 	$970,530 	$14,766 	$4,105 	$18,871 
3 	$955,702 	$14,827 	$4,044 	$18,871 
4 	$940,813 	$14,889 	$3,982 	$18,871 
5 	$925,862 	$14,951 	$3,920 	$18,871 
6 	$910,848 	$15,013 	$3,858 	$18,871 
7 	$895,772 	$15,076 	$3,795 	$18,871 
8 	$880,634 	$15,139 	$3,732 	$18,871 
9 	$865,432 	$15,202 	$3,669 	$18,871 
10 	$850,166 	$15,265 	$3,606 	$18,871 
11 	$834,837 	$15,329 	$3,542 	$18,871 
12 	$819,445 	$15,393 	$3,478 	$18,871 
13 	$803,988 	$15,457 	$3,414 	$18,871 
14 	$788,467 	$15,521 	$3,350 	$18,871 
15 	$772,881 	$15,586 	$3,285 	$18,871 
16 	$757,230 	$15,651 	$3,220 	$18,871 
17 	$741,514 	$15,716 	$3,155 	$18,871 
18 	$725,732 	$15,782 	$3,090 	$18,871 
19 	$709,885 	$15,847 	$3,024 	$18,871 
20 	$693,971 	$15,913 	$2,958 	$18,871 
21 	$677,992 	$15,980 	$2,892 	$18,871 
22 	$661,945 	$16,046 	$2,825 	$18,871 
23 	$645,832 	$16,113 	$2,758 	$18,871 
24 	$629,652 	$16,180 	$2,691 	$18,871 
25 	$613,404 	$16,248 	$2,624 	$18,871 
26 	$597,089 	$16,315 	$2,556 	$18,871 
27 	$580,706 	$16,383 	$2,488 	$18,871 
28 	$564,254 	$16,452 	$2,420 	$18,871 
29 	$547,734 	$16,520 	$2,351 	$18,871 
30 	$531,145 	$16,589 	$2,282 	$18,871 
31 	$514,487 	$16,658 	$2,213 	$18,871 
32 	$497,759 	$16,728 	$2,144 	$18,871 
33 	$480,962 	$16,797 	$2,074 	$18,871 
34 	$464,095 	$16,867 	$2,004 	$18,871 
35 	$447,157 	$16,938 	$1,934 	$18,871 
36 	$430,149 	$17,008 	$1,863 	$18,871 
37 	$413,070 	$17,079 	$1,792 	$18,871 
38 	$395,920 	$17,150 	$1,721 	$18,871 
39 	$378,698 	$17,222 	$1,650 	$18,871 
40 	$361,405 	$17,293 	$1,578 	$18,871 
41 	$344,040 	$17,365 	$1,506 	$18,871 
42 	$326,602 	$17,438 	$1,433 	$18,871 
43 	$309,092 	$17,510 	$1,361 	$18,871 
44 	$291,508 	$17,583 	$1,288 	$18,871 
45 	$273,852 	$17,657 	$1,215 	$18,871 
46 	$256,121 	$17,730 	$1,141 	$18,871 
47 	$238,317 	$17,804 	$1,067 	$18,871 
48 	$220,439 	$17,878 	$993 	$18,871 
49 	$202,486 	$17,953 	$918 	$18,871 
50 	$184,459 	$18,028 	$844 	$18,871 
51 	$166,356 	$18,103 	$769 	$18,871 
52 	$148,178 	$18,178 	$693 	$18,871 
53 	$129,924 	$18,254 	$617 	$18,871 
54 	$111,594 	$18,330 	$541 	$18,871 
55 	$93,188 	$18,406 	$465 	$18,871 
56 	$74,705 	$18,483 	$388 	$18,871 
57 	$56,145 	$18,560 	$311 	$18,871 
58 	$37,508 	$18,637 	$234 	$18,871 
59 	$18,793 	$18,715 	$156 	$18,871 
60 	$0 	$18,793 	$78 	$18,871 
Total			$132,274 	$1,132,274 

Code: Select all

FIXED PRINCIPAL				
Rate	5%			
Term (months)	 60 			
				
Period	Balance	Principal	Interest	Payment
0 	$1,000,000 			
1 	$983,333 	$16,667 	$4,167 	$20,833 
2 	$966,667 	$16,667 	$4,097 	$20,764 
3 	$950,000 	$16,667 	$4,028 	$20,694 
4 	$933,333 	$16,667 	$3,958 	$20,625 
5 	$916,667 	$16,667 	$3,889 	$20,556 
6 	$900,000 	$16,667 	$3,819 	$20,486 
7 	$883,333 	$16,667 	$3,750 	$20,417 
8 	$866,667 	$16,667 	$3,681 	$20,347 
9 	$850,000 	$16,667 	$3,611 	$20,278 
10 	$833,333 	$16,667 	$3,542 	$20,208 
11 	$816,667 	$16,667 	$3,472 	$20,139 
12 	$800,000 	$16,667 	$3,403 	$20,069 
13 	$783,333 	$16,667 	$3,333 	$20,000 
14 	$766,667 	$16,667 	$3,264 	$19,931 
15 	$750,000 	$16,667 	$3,194 	$19,861 
16 	$733,333 	$16,667 	$3,125 	$19,792 
17 	$716,667 	$16,667 	$3,056 	$19,722 
18 	$700,000 	$16,667 	$2,986 	$19,653 
19 	$683,333 	$16,667 	$2,917 	$19,583 
20 	$666,667 	$16,667 	$2,847 	$19,514 
21 	$650,000 	$16,667 	$2,778 	$19,444 
22 	$633,333 	$16,667 	$2,708 	$19,375 
23 	$616,667 	$16,667 	$2,639 	$19,306 
24 	$600,000 	$16,667 	$2,569 	$19,236 
25 	$583,333 	$16,667 	$2,500 	$19,167 
26 	$566,667 	$16,667 	$2,431 	$19,097 
27 	$550,000 	$16,667 	$2,361 	$19,028 
28 	$533,333 	$16,667 	$2,292 	$18,958 
29 	$516,667 	$16,667 	$2,222 	$18,889 
30 	$500,000 	$16,667 	$2,153 	$18,819 
31 	$483,333 	$16,667 	$2,083 	$18,750 
32 	$466,667 	$16,667 	$2,014 	$18,681 
33 	$450,000 	$16,667 	$1,944 	$18,611 
34 	$433,333 	$16,667 	$1,875 	$18,542 
35 	$416,667 	$16,667 	$1,806 	$18,472 
36 	$400,000 	$16,667 	$1,736 	$18,403 
37 	$383,333 	$16,667 	$1,667 	$18,333 
38 	$366,667 	$16,667 	$1,597 	$18,264 
39 	$350,000 	$16,667 	$1,528 	$18,194 
40 	$333,333 	$16,667 	$1,458 	$18,125 
41 	$316,667 	$16,667 	$1,389 	$18,056 
42 	$300,000 	$16,667 	$1,319 	$17,986 
43 	$283,333 	$16,667 	$1,250 	$17,917 
44 	$266,667 	$16,667 	$1,181 	$17,847 
45 	$250,000 	$16,667 	$1,111 	$17,778 
46 	$233,333 	$16,667 	$1,042 	$17,708 
47 	$216,667 	$16,667 	$972 	$17,639 
48 	$200,000 	$16,667 	$903 	$17,569 
49 	$183,333 	$16,667 	$833 	$17,500 
50 	$166,667 	$16,667 	$764 	$17,431 
51 	$150,000 	$16,667 	$694 	$17,361 
52 	$133,333 	$16,667 	$625 	$17,292 
53 	$116,667 	$16,667 	$556 	$17,222 
54 	$100,000 	$16,667 	$486 	$17,153 
55 	$83,333 	$16,667 	$417 	$17,083 
56 	$66,667 	$16,667 	$347 	$17,014 
57 	$50,000 	$16,667 	$278 	$16,944 
58 	$33,333 	$16,667 	$208 	$16,875 
59 	$16,667 	$16,667 	$139 	$16,806 
60 	$0 	$16,667 	$69 	$16,736 
Total			$127,083 	$1,127,083 
I believe this is the first time you have said "fixed principal", so that may have been the confusion between what you meant and what you were saying.

I'm not familiar with loans like this in the U.S. Anyone else? Do you have a link to a bank loan like this? I only see about a $5k difference between the two, so...

chevca
Posts: 2792
Joined: Wed Jul 26, 2017 11:22 am

Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by chevca » Wed Nov 06, 2019 5:10 pm

In a fixed principal or term loan as you list, what would extra payments even go towards... the balance, or just future payments? As in, you throw an extra $50k at it, does it just knock $50k off the balance that day, or does it go towards the next 5 or 6 payment paying both principal and the future interest?

chevca
Posts: 2792
Joined: Wed Jul 26, 2017 11:22 am

Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by chevca » Wed Nov 06, 2019 5:23 pm

I did a little Google searching for fixed principal loans and products and all I got was some definitions and calculators. So, it seems they are a thing. But, no ads or banks seem to be offering them. Granted, I only looked at page 1 of the search results.

Why are you asking about this? Do you have a loan like this?

delamer
Posts: 9057
Joined: Tue Feb 08, 2011 6:13 pm

Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by delamer » Wed Nov 06, 2019 5:28 pm

Clarice wrote:
Wed Nov 06, 2019 4:52 pm
Thanks for the help, all. Probably could have been a little clearer in the product type I was referencing. Better off paying amortizing loan before a fixed principal loan it looks like.

To the poster who said fixed-principal products don't exist in the US - I doubt that as it is more beneficial for the consumer.

Code: Select all

AMORTIZING				
Rate	5%			
Term (months)	 60 			
				
Period	Balance	Principal	Interest	Payment
0 	$1,000,000 			
1 	$985,295 	$14,705 	$4,167 	$18,871 
2 	$970,530 	$14,766 	$4,105 	$18,871 
3 	$955,702 	$14,827 	$4,044 	$18,871 
4 	$940,813 	$14,889 	$3,982 	$18,871 
5 	$925,862 	$14,951 	$3,920 	$18,871 
6 	$910,848 	$15,013 	$3,858 	$18,871 
7 	$895,772 	$15,076 	$3,795 	$18,871 
8 	$880,634 	$15,139 	$3,732 	$18,871 
9 	$865,432 	$15,202 	$3,669 	$18,871 
10 	$850,166 	$15,265 	$3,606 	$18,871 
11 	$834,837 	$15,329 	$3,542 	$18,871 
12 	$819,445 	$15,393 	$3,478 	$18,871 
13 	$803,988 	$15,457 	$3,414 	$18,871 
14 	$788,467 	$15,521 	$3,350 	$18,871 
15 	$772,881 	$15,586 	$3,285 	$18,871 
16 	$757,230 	$15,651 	$3,220 	$18,871 
17 	$741,514 	$15,716 	$3,155 	$18,871 
18 	$725,732 	$15,782 	$3,090 	$18,871 
19 	$709,885 	$15,847 	$3,024 	$18,871 
20 	$693,971 	$15,913 	$2,958 	$18,871 
21 	$677,992 	$15,980 	$2,892 	$18,871 
22 	$661,945 	$16,046 	$2,825 	$18,871 
23 	$645,832 	$16,113 	$2,758 	$18,871 
24 	$629,652 	$16,180 	$2,691 	$18,871 
25 	$613,404 	$16,248 	$2,624 	$18,871 
26 	$597,089 	$16,315 	$2,556 	$18,871 
27 	$580,706 	$16,383 	$2,488 	$18,871 
28 	$564,254 	$16,452 	$2,420 	$18,871 
29 	$547,734 	$16,520 	$2,351 	$18,871 
30 	$531,145 	$16,589 	$2,282 	$18,871 
31 	$514,487 	$16,658 	$2,213 	$18,871 
32 	$497,759 	$16,728 	$2,144 	$18,871 
33 	$480,962 	$16,797 	$2,074 	$18,871 
34 	$464,095 	$16,867 	$2,004 	$18,871 
35 	$447,157 	$16,938 	$1,934 	$18,871 
36 	$430,149 	$17,008 	$1,863 	$18,871 
37 	$413,070 	$17,079 	$1,792 	$18,871 
38 	$395,920 	$17,150 	$1,721 	$18,871 
39 	$378,698 	$17,222 	$1,650 	$18,871 
40 	$361,405 	$17,293 	$1,578 	$18,871 
41 	$344,040 	$17,365 	$1,506 	$18,871 
42 	$326,602 	$17,438 	$1,433 	$18,871 
43 	$309,092 	$17,510 	$1,361 	$18,871 
44 	$291,508 	$17,583 	$1,288 	$18,871 
45 	$273,852 	$17,657 	$1,215 	$18,871 
46 	$256,121 	$17,730 	$1,141 	$18,871 
47 	$238,317 	$17,804 	$1,067 	$18,871 
48 	$220,439 	$17,878 	$993 	$18,871 
49 	$202,486 	$17,953 	$918 	$18,871 
50 	$184,459 	$18,028 	$844 	$18,871 
51 	$166,356 	$18,103 	$769 	$18,871 
52 	$148,178 	$18,178 	$693 	$18,871 
53 	$129,924 	$18,254 	$617 	$18,871 
54 	$111,594 	$18,330 	$541 	$18,871 
55 	$93,188 	$18,406 	$465 	$18,871 
56 	$74,705 	$18,483 	$388 	$18,871 
57 	$56,145 	$18,560 	$311 	$18,871 
58 	$37,508 	$18,637 	$234 	$18,871 
59 	$18,793 	$18,715 	$156 	$18,871 
60 	$0 	$18,793 	$78 	$18,871 
Total			$132,274 	$1,132,274 

Code: Select all

FIXED PRINCIPAL				
Rate	5%			
Term (months)	 60 			
				
Period	Balance	Principal	Interest	Payment
0 	$1,000,000 			
1 	$983,333 	$16,667 	$4,167 	$20,833 
2 	$966,667 	$16,667 	$4,097 	$20,764 
3 	$950,000 	$16,667 	$4,028 	$20,694 
4 	$933,333 	$16,667 	$3,958 	$20,625 
5 	$916,667 	$16,667 	$3,889 	$20,556 
6 	$900,000 	$16,667 	$3,819 	$20,486 
7 	$883,333 	$16,667 	$3,750 	$20,417 
8 	$866,667 	$16,667 	$3,681 	$20,347 
9 	$850,000 	$16,667 	$3,611 	$20,278 
10 	$833,333 	$16,667 	$3,542 	$20,208 
11 	$816,667 	$16,667 	$3,472 	$20,139 
12 	$800,000 	$16,667 	$3,403 	$20,069 
13 	$783,333 	$16,667 	$3,333 	$20,000 
14 	$766,667 	$16,667 	$3,264 	$19,931 
15 	$750,000 	$16,667 	$3,194 	$19,861 
16 	$733,333 	$16,667 	$3,125 	$19,792 
17 	$716,667 	$16,667 	$3,056 	$19,722 
18 	$700,000 	$16,667 	$2,986 	$19,653 
19 	$683,333 	$16,667 	$2,917 	$19,583 
20 	$666,667 	$16,667 	$2,847 	$19,514 
21 	$650,000 	$16,667 	$2,778 	$19,444 
22 	$633,333 	$16,667 	$2,708 	$19,375 
23 	$616,667 	$16,667 	$2,639 	$19,306 
24 	$600,000 	$16,667 	$2,569 	$19,236 
25 	$583,333 	$16,667 	$2,500 	$19,167 
26 	$566,667 	$16,667 	$2,431 	$19,097 
27 	$550,000 	$16,667 	$2,361 	$19,028 
28 	$533,333 	$16,667 	$2,292 	$18,958 
29 	$516,667 	$16,667 	$2,222 	$18,889 
30 	$500,000 	$16,667 	$2,153 	$18,819 
31 	$483,333 	$16,667 	$2,083 	$18,750 
32 	$466,667 	$16,667 	$2,014 	$18,681 
33 	$450,000 	$16,667 	$1,944 	$18,611 
34 	$433,333 	$16,667 	$1,875 	$18,542 
35 	$416,667 	$16,667 	$1,806 	$18,472 
36 	$400,000 	$16,667 	$1,736 	$18,403 
37 	$383,333 	$16,667 	$1,667 	$18,333 
38 	$366,667 	$16,667 	$1,597 	$18,264 
39 	$350,000 	$16,667 	$1,528 	$18,194 
40 	$333,333 	$16,667 	$1,458 	$18,125 
41 	$316,667 	$16,667 	$1,389 	$18,056 
42 	$300,000 	$16,667 	$1,319 	$17,986 
43 	$283,333 	$16,667 	$1,250 	$17,917 
44 	$266,667 	$16,667 	$1,181 	$17,847 
45 	$250,000 	$16,667 	$1,111 	$17,778 
46 	$233,333 	$16,667 	$1,042 	$17,708 
47 	$216,667 	$16,667 	$972 	$17,639 
48 	$200,000 	$16,667 	$903 	$17,569 
49 	$183,333 	$16,667 	$833 	$17,500 
50 	$166,667 	$16,667 	$764 	$17,431 
51 	$150,000 	$16,667 	$694 	$17,361 
52 	$133,333 	$16,667 	$625 	$17,292 
53 	$116,667 	$16,667 	$556 	$17,222 
54 	$100,000 	$16,667 	$486 	$17,153 
55 	$83,333 	$16,667 	$417 	$17,083 
56 	$66,667 	$16,667 	$347 	$17,014 
57 	$50,000 	$16,667 	$278 	$16,944 
58 	$33,333 	$16,667 	$208 	$16,875 
59 	$16,667 	$16,667 	$139 	$16,806 
60 	$0 	$16,667 	$69 	$16,736 
Total			$127,083 	$1,127,083 
I’ve personally never had a loan that was fixed principal.

If you have, I’d be interested in knowing what it was for.

Topic Author
Clarice
Posts: 177
Joined: Thu Jun 14, 2018 3:26 pm
Location: Orlando FL

Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Wed Nov 06, 2019 5:34 pm

So all US consumer debt amortizes as I illustrated in the first option?

I’ve seen the second option with a small business loan. I think fixed principal might be common with floating interest rates.

alex_686
Posts: 5097
Joined: Mon Feb 09, 2015 2:39 pm

Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by alex_686 » Wed Nov 06, 2019 5:34 pm

Clarice wrote:
Wed Nov 06, 2019 4:52 pm
Thanks for the help, all. Probably could have been a little clearer in the product type I was referencing. Better off paying amortizing loan before a fixed principal loan it looks like. ...
The difference is driven by different cash flows, not "amortizing loan" vs. "fixed principal". So, here is my question to you: In the first loan you are paying $18,871 per month. In the second one you are initially paying 20,833 per month. To correctly evaluate the difference we need to equalize the cash flow and opportunity cost.

So, if you do take out loan #1, what are you going to do with the extra $1,962 in cash flow? The correct answer would be to apply that extra cash flow to pay down the principle.

On the flip side, if you take out loan #2, and when payments fall below that of loan #1 - where are you going to direct that extra cash flow? The correct answer - to keep apples to apples - would be back to a early pre-payment principle, and a reduction of interest charged.

So you would pay off both loans in the same time frame with the same amount of interest.

Like I suggested before, you need to look

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by alex_686 » Wed Nov 06, 2019 5:38 pm

Clarice wrote:
Wed Nov 06, 2019 5:34 pm
So all US consumer debt amortizes as I illustrated in the first option?

I’ve seen the second option with a small business loan. I think fixed principal might be common with floating interest rates.
The vast majority of debt, both personal or business. Any debt will "amortize" as you define it if they allow early payments of principle and interests is calculated off of the principle. Pre-payment penalties and interest charged under the "Rule of 78" makes things a bit more interesting and nuanced - but the principles still mostly hold.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by chevca » Wed Nov 06, 2019 5:39 pm

Clarice wrote:
Wed Nov 06, 2019 5:34 pm
So all US consumer debt amortizes as I illustrated in the first option?
Certainly the high majority of it is. I'm sure there are exceptions. But, the basic mortgage, auto, and personal loans are like your first option.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by nolesrule » Wed Nov 06, 2019 6:02 pm

alex_686 wrote:
Wed Nov 06, 2019 5:34 pm
The difference is driven by different cash flows, not "amortizing loan" vs. "fixed principal". So, here is my question to you: In the first loan you are paying $18,871 per month. In the second one you are initially paying 20,833 per month. To correctly evaluate the difference we need to equalize the cash flow and opportunity cost.

So, if you do take out loan #1, what are you going to do with the extra $1,962 in cash flow? The correct answer would be to apply that extra cash flow to pay down the principle.

On the flip side, if you take out loan #2, and when payments fall below that of loan #1 - where are you going to direct that extra cash flow? The correct answer - to keep apples to apples - would be back to a early pre-payment principle, and a reduction of interest charged.

So you would pay off both loans in the same time frame with the same amount of interest.

Like I suggested before, you need to look
With loan #2 the extra cash flow begins with the second payment, not when payments fall below loan #1.

Regardless, your overall point still stands.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Wed Nov 06, 2019 6:42 pm

nolesrule wrote:
Wed Nov 06, 2019 6:02 pm
alex_686 wrote:
Wed Nov 06, 2019 5:34 pm
The difference is driven by different cash flows, not "amortizing loan" vs. "fixed principal". So, here is my question to you: In the first loan you are paying $18,871 per month. In the second one you are initially paying 20,833 per month. To correctly evaluate the difference we need to equalize the cash flow and opportunity cost.

So, if you do take out loan #1, what are you going to do with the extra $1,962 in cash flow? The correct answer would be to apply that extra cash flow to pay down the principle.

On the flip side, if you take out loan #2, and when payments fall below that of loan #1 - where are you going to direct that extra cash flow? The correct answer - to keep apples to apples - would be back to a early pre-payment principle, and a reduction of interest charged.

So you would pay off both loans in the same time frame with the same amount of interest.

Like I suggested before, you need to look
With loan #2 the extra cash flow begins with the second payment, not when payments fall below loan #1.

Regardless, your overall point still stands.
Understood. Thanks for the help. Although I won’t take on that endeavor.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by grabiner » Wed Nov 06, 2019 8:37 pm

Clarice wrote:
Wed Nov 06, 2019 1:31 pm
If I have two loans with the same interest rate starting at exactly the same time, the amortizing loan has more interest dollars up front - so i would be better off paying that loan first.... no?
When rates are equal, it is better to pay down the shorter-term loan, but only because this gives you more options.

Suppose that you have a one-year loan and a ten-year loan, both at 4%. If you pay $1000 against either loan, your balance next year will be $1040 lower. If you made that payment against the ten-year loan, you can't get at that $1040 until the loan is paid off; you will get $1480 in ten years. If you made the payment against the one-year loan, you can spend the $1040 savings when the loan is paid off, or invest it in something else, or use it to make an extra payment against the ten-year (now nine-year) loan to get the same $1480 as if you had paid it against that loan in the first place.
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Thu Nov 07, 2019 7:32 am

grabiner wrote:
Wed Nov 06, 2019 8:37 pm
Clarice wrote:
Wed Nov 06, 2019 1:31 pm
If I have two loans with the same interest rate starting at exactly the same time, the amortizing loan has more interest dollars up front - so i would be better off paying that loan first.... no?
When rates are equal, it is better to pay down the shorter-term loan, but only because this gives you more options.

Suppose that you have a one-year loan and a ten-year loan, both at 4%. If you pay $1000 against either loan, your balance next year will be $1040 lower. If you made that payment against the ten-year loan, you can't get at that $1040 until the loan is paid off; you will get $1480 in ten years. If you made the payment against the one-year loan, you can spend the $1040 savings when the loan is paid off, or invest it in something else, or use it to make an extra payment against the ten-year (now nine-year) loan to get the same $1480 as if you had paid it against that loan in the first place.
Thank you - understood.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by celia » Thu Nov 07, 2019 11:00 am

OP, Why are minimum monthly payments in your two examples different from each other? How did you come up with those payment schedules?

Could it be that one also has insurance premiums tacked on to it to insure you make your payments? (This is common when taking out a mortgage and you put down less than 20%.)

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by chevca » Thu Nov 07, 2019 11:11 am

celia wrote:
Thu Nov 07, 2019 11:00 am
OP, Why are minimum monthly payments in your two examples different from each other? How did you come up with those payment schedules?
Look up fixed principal loans. I was not familiar with them either. But, the principal payment is all that is fixed. As the balance goes down, so does the interest part of the payment, and also the monthly payment adjusts down with it. The monthly payment amount is not fixed.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Meg77 » Thu Nov 07, 2019 11:22 am

Clarice wrote:
Thu Nov 07, 2019 7:32 am
grabiner wrote:
Wed Nov 06, 2019 8:37 pm
Clarice wrote:
Wed Nov 06, 2019 1:31 pm
If I have two loans with the same interest rate starting at exactly the same time, the amortizing loan has more interest dollars up front - so i would be better off paying that loan first.... no?
When rates are equal, it is better to pay down the shorter-term loan, but only because this gives you more options.

Suppose that you have a one-year loan and a ten-year loan, both at 4%. If you pay $1000 against either loan, your balance next year will be $1040 lower. If you made that payment against the ten-year loan, you can't get at that $1040 until the loan is paid off; you will get $1480 in ten years. If you made the payment against the one-year loan, you can spend the $1040 savings when the loan is paid off, or invest it in something else, or use it to make an extra payment against the ten-year (now nine-year) loan to get the same $1480 as if you had paid it against that loan in the first place.
Thank you - understood.
Hey there, OP! This is a SUPER common misconception even among people who work in finance. I'm a private banker and do lots of mortgages and I didn't even grasp this until a few years into my career.

Lots of people say that "you pay more interest at the beginning of a mortgage than at the end" which is technically correct but only because the balance is bigger at the beginning! You do NOT "prepay" interest on a mortgage or amortizing loan. The amount of interest you pay is always exactly equal to the prior month's balance multiplied by your interest rate. The payment stays the same, but each month you pay a little less in interest and a little more in principal - because the balance is reducing, not because of some fancy math.

So let's say you have a $50,000 5 year car loan at 4%. The monthly payment would be $920.83.
And let's say you have a $50,000 30 year mortgage at 4%. The monthly payment would be $238.71.

You pay the EXACT SAME AMOUNT OF INTEREST - $166.67 - on these loans in month one, when the balance is the same ($50K).

The only difference is that you pay a lot more principal on the car loan because the amortization is so much shorter.

So the bottom line is that interest is interest.

HOWEVER I do want to add that there ARE other things to consider if you're debating which loan to pay down first besides interest rate. Lots of studies have suggested that paying down the smaller balances first (even if the rate is a bit higher) gets people out of debt faster. The reason is behavioral, not mathematical. Seeing quicker progress by wiping out an entire debt sooner is highly motivating and can encourage people to stick with their debt reduction plans. Plus it frees up monthly payments sooner. This is why I paid off my 0% car loan first even though I have a 5.125% rental mortgage. I wiped out a big monthly payment which impacts me today, versus putting $20k against a mortgage which would still be there with it's required monthly payment tomorrow. Mathematically that doesn't make sense, but personal finance is personal. It's not always JUST about the math.
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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by Clarice » Thu Nov 07, 2019 12:07 pm

Meg77 wrote:
Thu Nov 07, 2019 11:22 am
Clarice wrote:
Thu Nov 07, 2019 7:32 am
grabiner wrote:
Wed Nov 06, 2019 8:37 pm
Clarice wrote:
Wed Nov 06, 2019 1:31 pm
If I have two loans with the same interest rate starting at exactly the same time, the amortizing loan has more interest dollars up front - so i would be better off paying that loan first.... no?
When rates are equal, it is better to pay down the shorter-term loan, but only because this gives you more options.

Suppose that you have a one-year loan and a ten-year loan, both at 4%. If you pay $1000 against either loan, your balance next year will be $1040 lower. If you made that payment against the ten-year loan, you can't get at that $1040 until the loan is paid off; you will get $1480 in ten years. If you made the payment against the one-year loan, you can spend the $1040 savings when the loan is paid off, or invest it in something else, or use it to make an extra payment against the ten-year (now nine-year) loan to get the same $1480 as if you had paid it against that loan in the first place.
Thank you - understood.
Hey there, OP! This is a SUPER common misconception even among people who work in finance. I'm a private banker and do lots of mortgages and I didn't even grasp this until a few years into my career.

Lots of people say that "you pay more interest at the beginning of a mortgage than at the end" which is technically correct but only because the balance is bigger at the beginning! You do NOT "prepay" interest on a mortgage or amortizing loan. The amount of interest you pay is always exactly equal to the prior month's balance multiplied by your interest rate. The payment stays the same, but each month you pay a little less in interest and a little more in principal - because the balance is reducing, not because of some fancy math.

So let's say you have a $50,000 5 year car loan at 4%. The monthly payment would be $920.83.
And let's say you have a $50,000 30 year mortgage at 4%. The monthly payment would be $238.71.

You pay the EXACT SAME AMOUNT OF INTEREST - $166.67 - on these loans in month one, when the balance is the same ($50K).

The only difference is that you pay a lot more principal on the car loan because the amortization is so much shorter.

So the bottom line is that interest is interest.

HOWEVER I do want to add that there ARE other things to consider if you're debating which loan to pay down first besides interest rate. Lots of studies have suggested that paying down the smaller balances first (even if the rate is a bit higher) gets people out of debt faster. The reason is behavioral, not mathematical. Seeing quicker progress by wiping out an entire debt sooner is highly motivating and can encourage people to stick with their debt reduction plans. Plus it frees up monthly payments sooner. This is why I paid off my 0% car loan first even though I have a 5.125% rental mortgage. I wiped out a big monthly payment which impacts me today, versus putting $20k against a mortgage which would still be there with it's required monthly payment tomorrow. Mathematically that doesn't make sense, but personal finance is personal. It's not always JUST about the math.
Thank you, Meg.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by dm200 » Thu Nov 07, 2019 12:09 pm

Lots of people say that "you pay more interest at the beginning of a mortgage than at the end" which is technically correct but only because the balance is bigger at the beginning! You do NOT "prepay" interest on a mortgage or amortizing loan. The amount of interest you pay is always exactly equal to the prior month's balance multiplied by your interest rate. The payment stays the same, but each month you pay a little less in interest and a little more in principal - because the balance is reducing, not because of some fancy math.
I am in this business as well.

In general, I agree. HOWEVER, there are many personal or consumer or auto loans where prepaid interest is charged on such loans. A "processing fee" charged on a loan with a credit union or bank is actually disclosed on the loan documents as a prepaid finance charge. Whenever there is a such disclosed prepaid finance charge - the Annual percentage rate disclosed is higher than the interest rate on the loan. Just one actual example of a short term (one year) loan given by a local credit union. The amount of such loans has to be $1,000 and for 12 months. The interest rate is 8.99% AND a 'fee' of $40 is charged at loan disbursement. That $40 is deducted from the $1,000. So, the borrower gets $960.00 in hand - but immediately has incurred a debt of $1,000. The loan documents show an APR (Annual Percentage Rate) much higher than 8.99 - depending on the date of the first payment due and the scheduled frequency of payments - the APR for these loans is in the 16.00 - 17.99% range. All this being said, if you already have one of these loans - the correct interest rate to look at is the 8.99% - the actual rate being charged/calculated whenever you make a payment.

Another "Boglehead" example analogous to someone asking what time it is -- and the answers received give detailed instructions on how to build a watch!

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by #Cruncher » Thu Nov 07, 2019 1:00 pm

Clarice wrote:
Wed Nov 06, 2019 2:16 pm
If I have a limited amount of money to prepay one loan or the other then I save more interest dollars today by paying towards the amortizing loan...
Assuming you're referring to the two 5% 60-month loans listed in this post, Clarice, you do indeed save more interest dollars by paying extra toward the one with the fixed total payment (what I believe you call an "amortizing" loan) rather than the one with the fixed principal payment. Using your example, if you pay $100,000 to reduce each $1,000,000 loan to $900,000, you'd save $13,227 interest on the first loan; but only $12,708 on the second loan.

However, while the savings on the first loan are spread evenly over the 60 months, more savings on the second loan occur during the first 30 months than during the last 30. Because of this, the Internal Rate of Return (IRR) from paying an additional $100,000 is the same (5%) for both loans. In fact the IRR is 5% for all six cases: the original $1,000,000 amount, the reduced $900,000 amount and the $100,000 reduction for both loans. [*] (The formulas use the Excel IRR function.)

Code: Select all

Fixed Total Payment Loan 
            Interest    IRR    Formula
   Original  132,274   5.00%  =12*IRR(B10:B70)
   Reduced   119,047   5.00%  =12*IRR(D10:D70)
   Savings    13,227   5.00%  =12*IRR(F10:F70)
Fixed Principal Payment Loan
            Interest    IRR    Formula
   Original  127,083   5.00%  =12*IRR(G10:G70)
   Reduced   114,375   5.00%  =12*IRR(I10:I70)
   Savings    12,708   5.00%  =12*IRR(K10:K70)
Here is the detail behind these numbers:

Code: Select all

   Col A       Col B     Col D     Col F        Col G     Col I     Col K
           -------------------  C a s h   F l o w s  --------------------
           ---- Fixed Total Pmt Loan ---    ---- Fixed Princ Pmt Loan ---
Row   Mo    Original   Reduced   Savings     Original   Reduced   Savings

Code: Select all

 10    0  (1,000,000) (900,000) (100,000)  (1,000,000) (900,000) (100,000)
 11    1      18,871    16,984     1,887       20,833    18,750     2,083 
 12    2      18,871    16,984     1,887       20,764    18,688     2,076 
 13    3      18,871    16,984     1,887       20,694    18,625     2,069 
 14    4      18,871    16,984     1,887       20,625    18,563     2,063
 15    5      18,871    16,984     1,887       20,556    18,500     2,056 
 16    6      18,871    16,984     1,887       20,486    18,438     2,049 
 17    7      18,871    16,984     1,887       20,417    18,375     2,042 
 18    8      18,871    16,984     1,887       20,347    18,313     2,035 
 19    9      18,871    16,984     1,887       20,278    18,250     2,028 
 20   10      18,871    16,984     1,887       20,208    18,188     2,021 
 21   11      18,871    16,984     1,887       20,139    18,125     2,014 
 22   12      18,871    16,984     1,887       20,069    18,063     2,007 
 23   13      18,871    16,984     1,887       20,000    18,000     2,000 
 24   14      18,871    16,984     1,887       19,931    17,938     1,993 
 25   15      18,871    16,984     1,887       19,861    17,875     1,986 
 26   16      18,871    16,984     1,887       19,792    17,813     1,979 
 27   17      18,871    16,984     1,887       19,722    17,750     1,972 
 28   18      18,871    16,984     1,887       19,653    17,688     1,965 
 29   19      18,871    16,984     1,887       19,583    17,625     1,958 
 30   20      18,871    16,984     1,887       19,514    17,563     1,951 
 31   21      18,871    16,984     1,887       19,444    17,500     1,944 
 32   22      18,871    16,984     1,887       19,375    17,438     1,938 
 33   23      18,871    16,984     1,887       19,306    17,375     1,931 
 34   24      18,871    16,984     1,887       19,236    17,313     1,924 
 35   25      18,871    16,984     1,887       19,167    17,250     1,917 
 36   26      18,871    16,984     1,887       19,097    17,188     1,910 
 37   27      18,871    16,984     1,887       19,028    17,125     1,903 
 38   28      18,871    16,984     1,887       18,958    17,063     1,896 
 39   29      18,871    16,984     1,887       18,889    17,000     1,889 
 40   30      18,871    16,984     1,887       18,819    16,938     1,882 
 41   31      18,871    16,984     1,887       18,750    16,875     1,875 
 42   32      18,871    16,984     1,887       18,681    16,813     1,868 
 43   33      18,871    16,984     1,887       18,611    16,750     1,861 
 44   34      18,871    16,984     1,887       18,542    16,688     1,854 
 45   35      18,871    16,984     1,887       18,472    16,625     1,847 
 46   36      18,871    16,984     1,887       18,403    16,563     1,840 
 47   37      18,871    16,984     1,887       18,333    16,500     1,833 
 48   38      18,871    16,984     1,887       18,264    16,438     1,826 
 49   39      18,871    16,984     1,887       18,194    16,375     1,819 
 50   40      18,871    16,984     1,887       18,125    16,313     1,813 
 51   41      18,871    16,984     1,887       18,056    16,250     1,806 
 52   42      18,871    16,984     1,887       17,986    16,188     1,799 
 53   43      18,871    16,984     1,887       17,917    16,125     1,792 
 54   44      18,871    16,984     1,887       17,847    16,063     1,785 
 55   45      18,871    16,984     1,887       17,778    16,000     1,778 
 56   46      18,871    16,984     1,887       17,708    15,938     1,771 
 57   47      18,871    16,984     1,887       17,639    15,875     1,764 
 58   48      18,871    16,984     1,887       17,569    15,813     1,757 
 59   49      18,871    16,984     1,887       17,500    15,750     1,750 
 60   50      18,871    16,984     1,887       17,431    15,688     1,743 
 61   51      18,871    16,984     1,887       17,361    15,625     1,736 
 62   52      18,871    16,984     1,887       17,292    15,563     1,729 
 63   53      18,871    16,984     1,887       17,222    15,500     1,722 
 64   54      18,871    16,984     1,887       17,153    15,438     1,715 
 65   55      18,871    16,984     1,887       17,083    15,375     1,708 
 66   56      18,871    16,984     1,887       17,014    15,313     1,701 
 67   57      18,871    16,984     1,887       16,944    15,250     1,694 
 68   58      18,871    16,984     1,887       16,875    15,188     1,688 
 69   59      18,871    16,984     1,887       16,806    15,125     1,681 
 70   60      18,871    16,984     1,887       16,736    15,063     1,674 
           --------- ---------   -------    --------- ---------   -------
   Total   1,132,274 1,019,047   113,227    1,127,083 1,014,375   112,708
mo  1-30     566,137   509,523    56,614      594,792   535,313    59,479 
mo 31-60     566,137   509,523    56,614      532,292   479,063    53,229 
Interest     132,274   119,047    13,227      127,083   114,375    12,708
* You'd expect the IRR to be same for the original amount, the reduced amount, and the savings for both loans since all the figures in the "Reduced" column are 90% of those in the "Original" column and all those in the "Savings" column are 10%.

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Re: Is the effective interest rate of a loan higher when it’s early in amortization period?

Post by dm200 » Thu Nov 07, 2019 1:33 pm

Being "in this business" - I commonly encounter, otherwise very intelligent, folks who get really mixed up about such matters.

A common situation I ran into was folks who were choosing to pay extra principal regularly on their home mortgage, while - at the same time - carrying balances on their credit card accounts - sometimes large balances.

When I would ask why they would pay extra on, say, a 5% mortgage loan - and carry a credit card at, say, 18% - the answer they gave me was that the mortgage was a much longer term - while they hoped/expected to pay off the credit card balances in a much shorter time. :confused :confused

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