During the amortization of a loan, the formula for repayment dictates
that early on, the overwhelming majority of payments are applied to
interest (as opposed to principal).  It's only much later on, towards
the end of the repayment period, that most of the payments are applied
to principal (as opposed to interest).

(For background, see http://en.wikipedia.org/wiki/Amortization_%28business%29 )


I'm trying to understand, fundamentally, why this is necessarily true.

Is it simply a matter of convention?  Is it because the lender
maximizes their profit this way?

Why, for example, could the amortization formula not have been
designed so that the ratios were constant over the life of the loan --
say, 60% interest vs. 40% principal for every payment?

Please note that I'm looking for a QUALITATIVE explanation, that
yields some insight into WHY amortization works the way it does.  Who
designed the formula this way, and why?

[And are there other common "repayment models", and what are they?]

Thanks.

---

Request for Question Clarification by richard-ga on 04 Feb 2006 09:19 PST

Hello:

I'm ready to answer your question, but I'm printing a table of numbers
here to see if it looks OK on Google Answers.  If it comes out as a
scrambled bunch of figures I'll have to rethink how I can present my
answer.

 100,000 	borrowed			
      6%	rate			
      15	years			
$10,296.28 	annual payment						
				
          owe	     int	   paid	       paydown
1	 100,000  6,000 	$10,296 	$4,296 
2	 95,704   5,742 	 10,296 	 4,554 
3	 91,150   5,469 	 10,296 	 4,827 
4	 86,322   5,179 	 10,296 	 5,117 
5	 81,205   4,872 	 10,296 	 5,424 
6	 75,781   4,547 	 10,296 	 5,749 
7	 70,032   4,202 	 10,296 	 6,094 
8	 63,938   3,836 	 10,296 	 6,460 
9	 57,478   3,449 	 10,296 	 6,848 
10	 50,630   3,038 	 10,296 	 7,258 
11	 43,372   2,602 	 10,296 	 7,694 
12	 35,678   2,141 	 10,296 	 8,156 
13	 27,522   1,651 	 10,296 	 8,645 
14	 18,877   1,133 	 10,296 	 9,164 
15	  9,713     583 	 10,296 	 9,713

---

Clarification of Question by rnd13-ga on 04 Feb 2006 09:21 PST

The table formats fine.  Please bear in mind, though, that I'm looking
for a *qualitative* answer ...

Hello and thank you for your question.

Please take a look at the Table that I posted above.
This describes a loan of $100,000 that is repaid in 15 equal, annual payments.
[Most mortgage loans are paid monthly, but the explanation is the same].

When the person who borrowed the money agreed to pay 6% interest on
the amount owed by the borrower during the term of the loan.

If they had only agreed to pay  .06 * $100,000 = $6,000 per year their
entire payment would be interest, in which case if they decided to pay
off the loan after 5 years the payoff amount would be the same
$100,000 that they borrowed at the start.

But the mortgage note that they signed contained an agreement to pay
$10,296.28 each year, meaning that the first year's payment (see line
#1) included a $4,296.28 overpayment, so to speak, which reduced their
debt after one year to
$95,704.

If after that first year they had gone to the bank and asked "what do
I owe you" the answer would be $95,704.  So the second year interest
paymentis the same amount that someone who borrows $95,704 at 6% has
to pay, $5,742.  So since in year two they're again paying  $10,296.28
[simply because that's the fixed payment that they undertook to pay
each year when they signed the note), there is that much more left
over ($4,554)to reduce the debt further.

The rest of the story is in the table.  That agreed-upon $10,296.28
happens to be the exact amount, paid in equal annual payments, that
leaves them owing nothing at the end of 15 years.

Thanks again for bringing us your question.  No google search for me
this time - - I used an Excel spreadsheet to generate the numbers that
you see.

The Table printed so nicely, I'm going to add a monthly amortization
of the same loan (see Clarification, below).  Here the person in
agreeing to the 6% rate has actually agreed to pay interest of .5% on
the balance owed at the time of each monthly payment of $843.86.

Again, I'm hoping the Table will print out OK.

Google Answers Researcher
Richard-ga

---

Clarification of Answer by richard-ga on 04 Feb 2006 09:42 PST

100,000 borrowed			
6%  rate  =0.5%	monthly	
15  years = 180	months	
$843.86 monthly payment			
				
        owe	     int	paid	paydown
1	 100,000 	 500 	$844 	$344 
2	 99,656 	 498 	 844 	 346 
3	 99,311 	 497 	 844 	 347 
4	 98,963 	 495 	 844 	 349 
5	 98,614 	 493 	 844 	 351 
6	 98,263 	 491 	 844 	 353 
7	 97,911 	 490 	 844 	 354 
8	 97,557 	 488 	 844 	 356 
9	 97,201 	 486 	 844 	 358 
10	 96,843 	 484 	 844 	 360 
11	 96,483 	 482 	 844 	 361 
12	 96,122 	 481 	 844 	 363 
13	 95,758 	 479 	 844 	 365 
14	 95,393 	 477 	 844 	 367 
15	 95,026 	 475 	 844 	 369 
16	 94,658 	 473 	 844 	 371 
17	 94,287 	 471 	 844 	 372 
18	 93,915 	 470 	 844 	 374 
19	 93,540 	 468 	 844 	 376 
20	 93,164 	 466 	 844 	 378 
21	 92,786 	 464 	 844 	 380 
22	 92,406 	 462 	 844 	 382 
23	 92,024 	 460 	 844 	 384 
24	 91,641 	 458 	 844 	 386 
25	 91,255 	 456 	 844 	 388 
26	 90,867 	 454 	 844 	 390 
27	 90,478 	 452 	 844 	 391 
28	 90,086 	 450 	 844 	 393 
29	 89,693 	 448 	 844 	 395 
30	 89,298 	 446 	 844 	 397 
31	 88,900 	 445 	 844 	 399 
32	 88,501 	 443 	 844 	 401 
33	 88,100 	 440 	 844 	 403 
34	 87,696 	 438 	 844 	 405 
35	 87,291 	 436 	 844 	 407 
36	 86,883 	 434 	 844 	 409 
37	 86,474 	 432 	 844 	 411 
38	 86,063 	 430 	 844 	 414 
39	 85,649 	 428 	 844 	 416 
40	 85,233 	 426 	 844 	 418 
41	 84,816 	 424 	 844 	 420 
42	 84,396 	 422 	 844 	 422 
43	 83,974 	 420 	 844 	 424 
44	 83,550 	 418 	 844 	 426 
45	 83,124 	 416 	 844 	 428 
46	 82,696 	 413 	 844 	 430 
47	 82,265 	 411 	 844 	 433 
48	 81,833 	 409 	 844 	 435 
49	 81,398 	 407 	 844 	 437 
50	 80,961 	 405 	 844 	 439 
51	 80,522 	 403 	 844 	 441 
52	 80,081 	 400 	 844 	 443 
53	 79,637 	 398 	 844 	 446 
54	 79,192 	 396 	 844 	 448 
55	 78,744 	 394 	 844 	 450 
56	 78,294 	 391 	 844 	 452 
57	 77,841 	 389 	 844 	 455 
58	 77,387 	 387 	 844 	 457 
59	 76,930 	 385 	 844 	 459 
60	 76,471 	 382 	 844 	 462 
61	 76,009 	 380 	 844 	 464 
62	 75,545 	 378 	 844 	 466 
63	 75,079 	 375 	 844 	 468 
64	 74,611 	 373 	 844 	 471 
65	 74,140 	 371 	 844 	 473 
66	 73,667 	 368 	 844 	 476 
67	 73,191 	 366 	 844 	 478 
68	 72,713 	 364 	 844 	 480 
69	 72,233 	 361 	 844 	 483 
70	 71,750 	 359 	 844 	 485 
71	 71,265 	 356 	 844 	 488 
72	 70,778 	 354 	 844 	 490 
73	 70,288 	 351 	 844 	 492 
74	 69,795 	 349 	 844 	 495 
75	 69,300 	 347 	 844 	 497 
76	 68,803 	 344 	 844 	 500 
77	 68,303 	 342 	 844 	 502 
78	 67,801 	 339 	 844 	 505 
79	 67,296 	 336 	 844 	 507 
80	 66,789 	 334 	 844 	 510 
81	 66,279 	 331 	 844 	 512 
82	 65,766 	 329 	 844 	 515 
83	 65,251 	 326 	 844 	 518 
84	 64,734 	 324 	 844 	 520 
85	 64,213 	 321 	 844 	 523 
86	 63,691 	 318 	 844 	 525 
87	 63,165 	 316 	 844 	 528 
88	 62,637 	 313 	 844 	 531 
89	 62,107 	 311 	 844 	 533 
90	 61,573 	 308 	 844 	 536 
91	 61,037 	 305 	 844 	 539 
92	 60,499 	 302 	 844 	 541 
93	 59,957 	 300 	 844 	 544 
94	 59,413 	 297 	 844 	 547 
95	 58,866 	 294 	 844 	 550 
96	 58,317 	 292 	 844 	 552 
97	 57,765 	 289 	 844 	 555 
98	 57,210 	 286 	 844 	 558 
99	 56,652 	 283 	 844 	 561 
100	 56,091 	 280 	 844 	 563 
101	 55,528 	 278 	 844 	 566 
102	 54,962 	 275 	 844 	 569 
103	 54,392 	 272 	 844 	 572 
104	 53,821 	 269 	 844 	 575 
105	 53,246 	 266 	 844 	 578 
106	 52,668 	 263 	 844 	 581 
107	 52,088 	 260 	 844 	 583 
108	 51,504 	 258 	 844 	 586 
109	 50,918 	 255 	 844 	 589 
110	 50,329 	 252 	 844 	 592 
111	 49,736 	 249 	 844 	 595 
112	 49,141 	 246 	 844 	 598 
113	 48,543 	 243 	 844 	 601 
114	 47,942 	 240 	 844 	 604 
115	 47,338 	 237 	 844 	 607 
116	 46,731 	 234 	 844 	 610 
117	 46,120 	 231 	 844 	 613 
118	 45,507 	 228 	 844 	 616 
119	 44,891 	 224 	 844 	 619 
120	 44,271 	 221 	 844 	 622 
121	 43,649 	 218 	 844 	 626 
122	 43,023 	 215 	 844 	 629 
123	 42,395 	 212 	 844 	 632 
124	 41,763 	 209 	 844 	 635 
125	 41,128 	 206 	 844 	 638 
126	 40,489 	 202 	 844 	 641 
127	 39,848 	 199 	 844 	 645 
128	 39,203 	 196 	 844 	 648 
129	 38,556 	 193 	 844 	 651 
130	 37,905 	 190 	 844 	 654 
131	 37,250 	 186 	 844 	 658 
132	 36,593 	 183 	 844 	 661 
133	 35,932 	 180 	 844 	 664 
134	 35,267 	 176 	 844 	 668 
135	 34,600 	 173 	 844 	 671 
136	 33,929 	 170 	 844 	 674 
137	 33,255 	 166 	 844 	 678 
138	 32,577 	 163 	 844 	 681 
139	 31,896 	 159 	 844 	 684 
140	 31,212 	 156 	 844 	 688 
141	 30,524 	 153 	 844 	 691 
142	 29,833 	 149 	 844 	 695 
143	 29,138 	 146 	 844 	 698 
144	 28,440 	 142 	 844 	 702 
145	 27,738 	 139 	 844 	 705 
146	 27,033 	 135 	 844 	 709 
147	 26,325 	 132 	 844 	 712 
148	 25,612 	 128 	 844 	 716 
149	 24,897 	 124 	 844 	 719 
150	 24,177 	 121 	 844 	 723 
151	 23,454 	 117 	 844 	 727 
152	 22,728 	 114 	 844 	 730 
153	 21,997 	 110 	 844 	 734 
154	 21,264 	 106 	 844 	 738 
155	 20,526 	 103 	 844 	 741 
156	 19,785 	 99 	 844 	 745 
157	 19,040 	 95 	 844 	 749 
158	 18,291 	 91 	 844 	 752 
159	 17,539 	 88 	 844 	 756 
160	 16,783 	 84 	 844 	 760 
161	 16,023 	 80 	 844 	 764 
162	 15,259 	 76 	 844 	 768 
163	 14,491 	 72 	 844 	 771 
164	 13,720 	 69 	 844 	 775 
165	 12,945 	 65 	 844 	 779 
166	 12,166 	 61 	 844 	 783 
167	 11,383 	 57 	 844 	 787 
168	 10,596 	 53 	 844 	 791 
169	  9,805 	 49 	 844 	 795 
170	  9,010 	 45 	 844 	 799 
171	  8,211 	 41 	 844 	 803 
172	  7,408 	 37 	 844 	 807 
173	  6,601 	 33 	 844 	 811 
174    	  5,791 	 29 	 844 	 815 
175	  4,976 	 25 	 844 	 819 
176	  4,157 	 21 	 844 	 823 
177	  3,334 	 17 	 844 	 827 
178	  2,506 	 13 	 844 	 831 
179	  1,675 	 8 	 844 	 835 
180	  840 	         4       844 	 840

---

Request for Answer Clarification by rnd13-ga on 04 Feb 2006 10:53 PST

OK, I think I'm getting it now.  The key seems to be that the payments
are constant, while the balance (principal) is declining.  Makes more
sense now.


But to follow up, if this is the "simplest repayment model", according
to Wikipedia ... then what other "repayment models" are there?

And to use my example, is a constant ratio model, if you will, (e.g.,
60% interest vs. 40% principal for every payment) ever used in
practice?

Lastly, who designed the constant payment model?  I'm told it came
about in the 1930s, to allow people to buy houses in installments. 
Any further details?  (And for extra credit, how was home buying done
before this?)

Thanks in advance!

---

Clarification of Answer by richard-ga on 04 Feb 2006 14:34 PST

Hello again

That's right, if the payments are constant and are greater in amount
that the current interest on the unpaid balance, that balance
(principal) will decline by application of the excess.

The simplest repayment model is no repayment until the end of the
term.  That is, the repayment promise is to pay interest monthly (or
annually, etc.) on the unpaid balance, with the entire principal due
at the end of a stated term.

I'm not sure how 60% interest vs. 40% principal for every payment
would work, because as soon as you pay any principal the next payment
will call for less interest.

I can't tell you anything about who designed the constant payment
model nor when it came about.  You should consider posting that as a
new question at whatever price you think is appropriate, which will
give other Researchers a chance to help you.

Regards,
Richard-ga

A bit more quantitative than I would have liked, but it did convey the
essence of what I was looking for.  Thanks!

MD13 --

You're paying periodic (monthly) interest on a standing balance, which
declines by the small amount of the principal each month.  This little
Java application shows it graphically:
Karl Jeacle's Mortgage Calculator
http://www.jeacle.ie/mortgage/

Best regards,

Omnivorous-GA

Well, ask and ye shall receive ...

Found out a lot of specifics about the origins with a simple Google search:
://www.google.com/search?client=safari&rls=en-us&q=constant+payment+1930s

Thanks again!