EXAMPLE 3 Interest Compounded Quarterly

Suppose again, as in Example 1, that you have $1000 deposited at 10% annual interest, but this time with interest compounded quarterly. How much is in the account at the end of one year?

At the end of the first quarter, you have the original balance plus $25 interest, so the balance at the beginning of the second quarter is $1025. During the second quarter, you receive interest equal to 2.5% of $1025, or $25.625, which is rounded up in posting to your account (since the fraction is half a cent or more) to $25.63. Continuing in this manner, the balance at the end of the first year is $1 103.82; see Table 21.1. (You should confirm all calculations in this chapter on your calculator.)

Even though the account was advertised as paying 10% interest, the interest for the year is $103.82, which is 10.382% of the original principal of $1000.