Copyright © 2008, The McGraw-Hill Companies, Inc.
You can (and should) verify the third and fourth rows of the table by repeating these steps
for those payments.Some Key Points about Amortization
Beyond being able to fill in the rows and columns of an amortization table, there are some
key points worth noting about amortization.The amount of each payment is the same, but the split between interest and principal
changes with each payment.
As the balance is paid down, the portion of each payment dedicated to interest
declines. A larger share of early payments will thus go toward interest than later
payments.
As interest’s share of the payments decreases, principal’s share of the payments
increases. So not only does each payment reduce the amount owed, but also the pace
of the reduction is accelerating. The fi rst payment killed off $221.92, but the last pay-
ment wiped out $279.56.
We might have expected that the interest would be compound interest, but notice that,
since each payment must cover the entire amount of interest for the period, interest
never gets a chance to compound upon itself.Example 4.5.1 Pat and Tracy (from Examples 4.4.8 and 4.4.9) took out a 30-year
loan for $158,000 at 7.2%. Their monthly payment was $1,072.49. Complete an
amortization table for their fi rst 12 monthly payments.For the fi rst month, interest would be paid on the full $158,000, so the interest would be
I ($158,000)(0.072)(1/12) $948.00. This leaves $1,072.49 $948.00 $124.49
to go toward reducing principal, and so after this payment they will owe $158,000
$124.49 $157,875.51.The calculations for the next month are similar, except that instead of using $158,000 we
instead use the slightly smaller $157,875.51. Because this is smaller, it requires less inter-
est, increasing the amount that is left for principal. As expected, this trend continues in the
ensuing months as well.Payment
NumberPayment
AmountInterest
AmountPrincipal
AmountRemaining
Balance1 $1,072.49 $948.00 $124.49 $157,875.51
2 $1,072.49 $947.25 $125.24 $157,750.27
3 $1,072.49 $946.50 $125.99 $157,624.28
4 $1,072.49 $945.75 $126.74 $157,497.54
5 $1,072.49 $944.99 $127.50 $157,370.04
6 $1,072.49 $944.22 $128.27 $157,241.77
7 $1,072.49 $943.45 $129.04 $157,112.73
8 $1,072.49 $942.68 $129.81 $156,982.92
9 $1,072.49 $941.90 $130.59 $156,852.33
10 $1,072.49 $941.11 $131.38 $156,720.95
11 $1,072.49 $940.33 $132.16 $156,588.79
12 $1,072.49 $939.53 $132.96 $156,455.83We used Pat and Tracy’s mortgage before, in the previous section, where we compared the
payment on a 30-year mortgage to the payment on a 15-year loan. Looking at the amortiza-
tion table now, we can start to see why the payment didn’t need to be that much larger for
the 15-year loan. Interest is based entirely on the amount owed, and so the “extra” money
in the payment does not go toward any extra interest. The extra goes entirely to principal.
An amortization table can help illustrate this:4.5 Amortization Tables 183cb