## Entrepreneurship UniversityA Course in Personal Financial Planning

### TVM: Loan Amortization

#### Amortization

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.