Amortization is a method for repaying a loan in equal installments. Part of each payment goes toward interest due
for the period and the remainder is used to reduce the principal (the loan balance). As the balance of the loan
is gradually reduced, a progressively larger portion of each payment goes toward reducing principal.
For Example, the 15 and 30 year fixed-rate mortgages common in the US are fully amortized loans. To pay off a
$100,000, 15 year, 7%, fixed-rate mortgage, a person must pay $898.83 each month for 180 months (with a small adjustment
at the end to account for rounding). $583.33 of the first payment goes toward interest and $315.50 is used
to reduce principal. But by payment 179, only $10.40 is needed for interest and $888.43 is used to reduce principal.
Amortization Schedule
An amortization schedule is a table with a row for each payment period of an amortized loan. Each row shows the amount
of the payment that is needed to pay interest, the amount that is used to reduce principal, and the balance of the loan
remaining at the end of the period.
The first and last 5 months of an amortization schedule for a $100,000, 15 year, 7%, fixed-rate mortgage will look like this:
Amortization Schedule
Month
Principal
Interest
Balance
1
-315.50
-583.33
99,684.51
2
-317.34
-581.49
99,367.17
3
-319.19
-579.64
99,047.98
4
-321.05
-577.78
98,726.93
5
-322.92
-575.91
98,404.01
Rows 6-175 omitted
176
-873.07
-25.76
3,543.48
177
-878.16
-20.67
2,665.32
178
-883.28
-15.55
1,782.04
179
-888.43
-10.40
893.61
180
-893.62
-5.21
-0.01
Exercise: Generate the table above in
Excel.
Negative Amortization
Negative amortization occurs when the payment is not large enough to cover the interest due for a period.
This will cause the loan balance to increase after each payment - a situation that should certainly be avoided.
This might occur, for instance, if the rate of an adjustable-rate loan increases, but the payment does not.
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