“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).

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