Lucy deposited 62500 in an investment fund th… | GMAT Sprint

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PS · Problem Solving

705-805

percent

Lucy deposited $62500 in an investment fund that provided 16 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $5100?

Correct answer marked below

0.5

Correct

6.1

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Explanation

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Official Explanation

Official

We use the compound interest formula:

A = P(1 + \frac{r}{n \cdot 100})^{n \cdot t}

.

Given:

P = 62500

I = 5100

, so

A = P + I = 62500 + 5100 = 67600

.

Annual rate

r = 16

, compounded quarterly so

n = 4

.

We need time

t

in years, then convert to months.

Plug into the formula:

67600 = 62500(1 + \frac{16}{4 \cdot 100})^{4t}

67600 = 62500(1 + \frac{1}{25})^{4t}

…

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What this question 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.

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