## 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 . 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

.

The interest earned in 3 months is .

*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

.

The balance after one year would be .

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

.