# Simple and Compound Interest on the GMAT

Occasionally on the GMAT, word problems involving simple and compound interest pop up. Interest can be thought of as the rental cost of money. The math requires a solid grasp of percentages and exponents. Like Rates and Work questions, this concept can appear intimidating if you don’t know the required formulas, but are actually fairly simple to solve!

There are only a few major formulas to know to get better scores on these GMAT questions. The first is simple interest earned during a time period t:  P*r*t, where P = starting principal, r = the annual rate, and t = the number of years of accrual. Future value under simple interest would be calculated as: A=P(1+rt).

For example, to find how much would be in an account after 3 years with an initial investment of \$500 at an annual rate of 6% simple interest:  500*.06*3 = \$90. So the balance would be \$590.

For finding the future value under compound interest, the formula is P (1 + r)t where P is the starting principal, r is simply the annual rate, and t is the number of years of accrual. A variant of this is P(1 + r/x)xt , where x = the number of times the principal compounds per year and r = the nominal annual rate. Think of the formula like:

FutureValue = PresentValue (1 + InterestPerPeriod)^(NumberOfPeriods)

If the interest only compounds once a year then x =1. If the interest compounds “semi-annually” then x = 2. If the interest compounds “quarterly” then x = 4, and if the interest compounds “monthly” then x = 12.  Here’s how to apply out formula to a sample question:

Julia decided to open an account at her local bank to save for a vacation to Hawaii. She invested \$1,000 at an interest rate of 5.6% compounded annually. How much would Julia’s investment be worth after three years?

The formula for compound interest is P (1 + r)t where P is the starting principal, r is the annual rate, and t is the number of years of accrual. For the first customer, we can plug in the values as follows: P(n) = 1,000 (1 + .056)3, which becomes approximately \$1178 after three years.

Interest can also appear in Data Sufficiency questions! Let’s look at a simple interest question from the GMAT Official Guide:

If \$5,000 invested for one year at p percent simple annual interest yields \$500, what amount must be invested at k percent simple annual interest for one year to yield the same number of dollars?

(1) k = 0.8p
(2) k = 8

The phrase “what amount” tells us this is a Value questions. \$500 = \$5,000*p/100*1 is another way of saying, what percentage of \$5,000 is \$500? The rate must be 10%, or p =10.

\$500 = P*k/100*1

We need to know what k is, to find P. Statement (2) is obviously sufficient. Statement (1) is also sufficient, since we know p = 10, k must be .8(10) = 8.