GRE Math : How to find compound interest

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Find Compound Interest

A five-year bond is opened with  in it and an interest rate of %, compounded annually. This account is allowed to compound for five years. Which of the following most closely approximates the total amount in the account after that period of time?

Possible Answers:

Correct answer:


Each year, you can calculate your interest by multiplying the principle () by . For one year, this would be:

For two years, it would be:

, which is the same as 

Therefore, you can solve for a five year period by doing:

Using your calculator, you can expand the  into a series of multiplications. This gives you , which is closest to 

Example Question #1 : Pattern Behaviors In Exponents

Jack has , to invest. If he invests two-thirds of it into a high-yield savings account with an annual interest rate of , compounded quarterly, and the other third in a regular savings account at  simple interest, how much does Jack earn after one year?

Possible Answers:

Correct answer:


First, break the problem into two segments: the amount Jack invests in the high-yield savings, and the amount Jack invests in the simple interest account (10,000 and 5,000 respectively).

Now let's work with the high-yield savings account. $10,000 is invested at an annual rate of 8%, compounded quarterly. We can use the compound interest formula to solve:

Plug in the values given:

Therefore, Jack makes $824.32 off his high-yield savings account. Now let's calculate the other interest:


Add the two together, and we see that Jack makes a total of,  off of his investments.

Example Question #11 : Gre Quantitative Reasoning

If a cash deposit account is opened with  for a three year period at % interest compounded once annually, which of the following is closest to the positive difference between the interest accrued in the third year and the interest accrued in the second year?

Possible Answers:

Correct answer:


It is easiest to break this down into steps. For each year, you will multiply by  to calculate the new value. Therefore, let's make a chart:

After year 1: ; Total interest: 

After year 2: ; Let us round this to ; Total interest: 

After year 3: ; Let us round this to ; Total interest: 

Thus, the positive difference of the interest from the last period and the interest from the first period is: 

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