EXAMPLE 8 A Savings Plan

A graduate at her first job saves $100 per month, deposited directly into her credit union account on payday, the last day of the month. The account earns 1.8% per year, compounded monthly. How much will she have at the end of five years, assuming that the credit union continues to pay the same interest rate?

883

She makes the first deposit at the end of the first month and the last deposit at the end of the 60th month. The monthly interest rate is .

It’s easier to look at the deposits in reverse time order. The last deposit is made on the last day of the five years, so it earns no interest and contributes just $100 to the total.

The second-last deposit earns interest for one month, contributing . Similarly, the third-last contribution is on deposit for two months, contributing .

Continuing in the same way, we find that the first deposit earns interest for 59 months and contributes . The total of all of the contributions is

We will return to this example after developing a formula needed for the solution.