Skill 39
Calculating Simple and Compound Interest

When you borrow money from a bank or take out a mortgage or a car loan, you have to pay interest. When you put money in a savings account or an interest-bearing checking account, you earn interest on it for as long as the money stays in the account. There are two basic kinds of interest, simple and compound.

Simple Interest. Let’s say you borrow $10,000 to purchase a used car. The bank lends you that money (called the principal), but says that in order to have it, you must pay 5% interest on that principal sum every year.

You want to know how much interest you will have to pay on that original $10,000 in year 1 of your loan if you don’t pay back any part of the principal. This kind of interest, calculated only on the principal, is called simple interest. You calculate simple interest using this formula:

Interest = Principal × Rate × Time

In this example, interest = $10,000 × 5% × 1 year. Calculate: $10,000 × 0.05 × 1 = $500. So you would owe $500 in interest for year 1. If you paid off the loan at the end of that year, you would have to pay a total of $10,500.

Here is another example. Suppose you put $5,000 in a savings account at 3% annual interest. How much would you have after 1 year?

Interest = Principal × Rate × Time

Interest = $5,000 × 0.03 × 1 = $150, so after one year your account would be worth $5,000 + $150 = $5,150.

On the ASVAB, you might get a problem that is not so straightforward. Perhaps you will be asked to calculate the rate of interest rather than the amount. Here is an example. On January 1 you put $6,000 in an interest-bearing savings account. On December 31 of that year, your balance was $6,120. What was the rate of interest?

The amount of interest you earned was $6,120 − $6,000 (the principal) = $120.

Compound Interest. Unlike simple interest, compound interest is calculated on the sum of the principal and any interest already earned. This sum increases (“compounds”) regularly as more interest is added. You calculate compound interest using the same formula, but you apply the rate of interest to the new total every time the sum increases.

Here is an example. Suppose you put $5,000 in a fund that earns you 5% interest compounded annually. What would your balance be at the end of 3 years?

Year 1: $5,000 × 0.05 × 1 = $250 (interest earned)

End-of-Year Balance = $5,250

Year 2: $5,250 × 0.05 × 1 = $262.50 (interest earned)

End-of-Year Balance = $5,512.50

Year 3: $5,512.50 × 0.05 × 1 = $275.63 (interest earned)

End-of-Year Balance = $5,788.13

Test Yourself!

You place $1,500 in an interest-bearing checking account that earns 2.5% annual interest. What will your balance be at the end of 1 year?

You place $2,200 in an account that earns 3% interest compounded annually. How much will your balance be at the end of 4 years?

You place $2,200 in an account that earns 3% interest compounded annually. If you are saving for a computer that costs $2,500, at the end of what year would you have enough money in this account?