## GMAT Interest Rate Questions: A Beginner’s Guide

Most people understand that when their money lives in an interest-bearing account, it grows over time. That’s simple enough. However, interest rate questions on the GMAT are a bit trickier and have more moving parts. Before we dive into any examples, let’s take a step back and review the two types of interest rates you should be prepared to handle on the GMAT.

## Simple interest

Simple interest is exactly that: simple.

In fact, most students learn how simple interest works fairly early in life. Imagine that you’ve been given $500 to put into a savings account that yields 5% interest yearly for 5 years (an unrealistic rate in most cases, but we’ll use this for the sake of the example). Simple interest would dictate in this instance that you would be paid $25 in interest every year for the next 5 years, giving you a total of $625 at the end of that term. You won’t need a complicated formula to understand how it works, and because it’s so straightforward, it almost seems ideal on a practical level.

However, for reference, here is the formula for simple interest:

- = the dollar amount of your investment after all interest has been paid
- = the principal, or the amount of money you initially invested
- = the interest rate (as a decimal)
- = the number of years you’ve agreed to invest for

However, the GMAT will be more interested in your understanding of compound interest, for which there is a formula and far more working parts to understand.

## Compound interest

Unlike simple interest, compound interest pays a percentage on not only your initial investment, but also on any interest you’ve already been paid. In other words, compound interest pays interest on interest.

Of course, you could use the process we discussed above to determine how much interest you’ll be paid over, except you’ll need to calculate the new balance every time a payout period lapses. This, as you can probably guess, would take more time than you’d like to spend on the GMAT. To save yourself a great deal of time (and avoid unnecessary frustration), remember this formula on test day:

As we alluded to, there are a number of working parts to the compound interest formula:

- = the dollar amount of your investment after all interest has been paid
- = the amount of money you initially invested
- = the interest rate (as a decimal)
- = the number of times the interest rate is compounded (occurs) in a given year (note that this is not part of the simple interest formula)
- = the number of years you’ve agreed to invest for

To illustrate how this formula works, let’s consider some of the numbers we used earlier in the following example.

If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years?

A) $750.00

B) $823.50

C) $973.25

D) $1000.25

E) $1100.00

Let’s quickly outline the information we know: $500 is the initial investment (*P*), our annual interest rate is 0.05% (*r*) , occurring once a month or 12 times per year (*n*) for 10 years (*t*). Now that we understand what we’re working with, let’s plug this information into the compound interest formula.

Plugging this equation into a calculator quickly tells us that after 10 years, we would be left with $823.50, making B the correct answer.

There’s just one problem, of course: we are not allowed to use a calculator on the Quant portion of the GMAT. So, how would we be able to arrive at the correct answer of $823.50?

Economist GMAT Tutor’s strategy for calculating compound interest rate problems that ask for a value is to calculate the amount using the simple interest formula and then choose an answer which is slightly higher. Indeed, compound interest pays out a higher amount, so using this approach would get us to the correct answer.

For the example above, we could use the simple interest formula and obtain:

=

=

=

And we see that answer choice A is $750, but alas, this is not the correct answer, since this is the result for simple interest and the question asks for compound interest.

Since compound interest delivers a higher yield, we can select the next higher answer choice B, $823.50, which is the correct answer.

The good news, however, is that you will only receive one interest rate problem on the GMAT.

And for the one interest rate problem that you will receive, the question may not ask you to calculate an exact value but instead ask, ‘Which of the following is the approximate value of the investment?’

Further, the interest rate question may simply ask you to select an answer which is just a version of the formula and you have to find the one with the correct numbers or variables in place.

To sum it up, interest rate questions on the GMAT might be worded in a tricky way and present different challenges than our example, but if you take the time to get comfortable with the compound interest formula and the strategy we’ve discussed here, you’ll be more than prepared to tackle these questions on test day.

*This post appeared first on the **Economist GMAT Tutor** blog.*

## 2 comments

Jan on October 17th, 2015 at 9:29 am

Dear Sir/Madam,

I am very new for GMAT and I am just starting to prepare for that. I have a difficulty in understanding the following question.

Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?

A. 90

B.82

C.80.

D.45

E.36

Toby Okonkwo on April 26th, 2017 at 5:58 pm

The formula for the compound interest doesn't clearly show the exponent. looks like it's a multiplication.