Compound Interest on the GMAT

“Compound interest” occurs when interest earned is added to the principal, which then earns interest. If you’re an investor, compound interest is a very good thing! Usually interest appears on the GMAT in the form of a word problem. Let’s solve one together!

An amount is deposited into an account accruing interest annually at a fixed percentage rate. It is valued at $900 in the third year (after interest has compounded twice), and $1080 in the fourth year (after interest has compounded three times). What is the original amount?

A) 540
B) 600
C) 625
D) 750
E) 800

To calculate the amount earned under compound interest under a certain period of time, you need to know three pieces of information: 1) the initial principle “P”, 2) the rate of interest “R”, and 3) the number of times it compound per year. You will always raise the rate to a power equal to the number of times it compounds.

For example, the amount in an account started with an initial investment of $200 and earning compound interest at a rate of 8% compounded three times a year would be found by the equation:

1 + (8/100)^3 * 200 = Final Amount

Knowing this, we can set up these formulas with the given information from this problem:

(1+(R/100)^2)*P = 900
(1+(R/100)^3)*P = 1080

We can put R/100 so that the R will be the percent and not a decimal. Then we can divide the 2nd equation by the 1st to get:

(1+ R/100)= 1080/900
1 + R/100 = 1.2

Now we can plug in 1.2 for (1 + R/100) into our original equation to find the “original amount”:

1.2^2*P = 900
1.44 * P = 900
P = 900/1.44
P = 625

The answer is (C).