A certain investment grows at an annual inter… | GMAT Sprint

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PS · Problem Solving

705-805

percent

A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?

Answer Choices

Correct answer marked below

16 =

1.02^{x/4}

2 =

1.02^x

Correct

16 =

1.08^{4x}

2 =

1.02^{x/4}

\frac{1}{16}

1.02^{4x}

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Explanation

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Official Explanation

Official

If we apply 8% annual interest, compounded quarterly, then we apply one quarter of the interest (or 2% interest) four times per year.

That is, in one year, we will multiply the value of our investment by 1.02 four times, or in other words, by

(1.02)^4

.

So, if we invest for x years, we will apply 2% interest 4x times, so will multiply the value of our initial investment by

(1.02)^{4x}

.…

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What this question tests

What it tests

Your ability to apply GMAT math concepts to solve a multi-step problem quickly and accurately. At the 705-805 level, accuracy and speed both matter.

Common trap

Overcomplicating the setup — most GMAT problems reward a direct, organized approach over brute calculation.