## Definition of Amortize a Loan

To amortize a loan usually means establishing a series of equal monthly payments that will provide the lender with:

- An
*interest*payment based on the unpaid principal balance as of the beginning of the month - A
*principal payment*that will cause the unpaid principal balance to decrease each month so that the principal balance will be zero at the time of the final payment

Although the total amount of each monthly payment remains the same, interest and principal payments will be changing as follows:

- The interest component of each monthly payment will be decreasing (because of the monthly decline in the principal balance)
- The principal component of each monthly payment will be increasing

A listing of each month's interest and principal payments along with the remaining, unpaid principal balance after each payment is known as an amortization schedule.

## Example of Amortizing a Loan

Assume that a lender proposes to amortize a $60,000 loan at 4% annual interest over a 3-year period. This will require 36 monthly payments of $1,771.44 each. The first two payments will consist of the following:

- Interest payment of $200.00 ($60,000 X 4% X 1/12) plus a principal payment of $1,571.44. After this payment, the principal balance will be $58,428.56 ($60,000.00 - $1,571.44)
- Interest payment of $194.76 ($58,428.56 X 4% X 1/12) plus a principal payment of $1,576.68. After this payment the principal balance will be $56,851.88 ($58,428.56 - $1,576.68)

The 36th and final monthly payment of $1,771.44 will consist of interest of $5.89 (the principal balance after the 35th payment of $1,765.55 X 4% X 1/12) plus a principal payment of $1,765.55. After the 36th payment the loan balance will be zero. In other words, the loan will have been amortized over its 3-year term.