Bob invested one half of his savings in a bon… | GMAT Sprint

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PS · Problem Solving

705-805

percent

Bob invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest?

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Explanation

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Official Explanation

Official

For the first year, Simple Interest and Compound Interest will always be the same if compounding is done annually.

So, the difference

605 - 550 = 55

is attributed to the interest earned on the first year's interest in the Compound Interest account.

Let the half savings amount be

P

.

Simple interest for 2 years:

P \times R \times 2 / 100 = 550

→

P = \frac{27500}{R}

.

Compound interest for 2 years:

P(1 + R/100)^2 - P = 605

.

But a quicker way: The extra

55

comes from interest on the first year's interest of the compound account.…

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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.