GMAT Quantitative Review

3.0 Math Review

3.4 Word Problems

4. Interest Problems

Interest can be computed in two basic ways. With simple annual interest, the interest is computed on the principal only and is equal to image. If interest is compounded, then interest is computed on the principal as well as on any interest already earned.

Example 1: If $8,000 is invested at 6 percent simple annual interest, how much interest is earned after 3 months?

Solution: Since the annual interest rate is 6%, the interest for 1 year is

image.

The interest earned in 3 months is image.

Example 2: If $10,000 is invested at 10 percent annual interest, compounded semiannually, what is the balance after 1 year?

Solution: The balance after the first 6 months would be

image.

The balance after one year would be image.

Note that the interest rate for each 6-month period is 5%, which is half of the 10% annual rate. The balance after one year can also be expressed as

image.