“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?
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).