On the first of the year, James invested x dollars at Proudstar bank in an account that yields

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On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?

A. 2.04%
B. 6.12%
C. 8%
D. 8.25%
E. 10%


OA D

Source: Princeton Review

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There are several issues with the question. For one thing ,we don't know if the interest on the first account is simple interest or compound interest. If the account earns 2% simple interest every quarter year, it will earn 8% interest in a full year, and the answer is C. If instead the interest compounds, then it will earn slightly more than if it doesn't, so D should be right. But D isn't mathematically the right answer here. If an investment earns 2% interest, its value is multiplied by 1.02, so if it earns 2% four times, its value will be multiplied by 1.02^4. Using a calculator, that's roughly equal to 1.08243, so the investment earns approximately 8.24% in a year, and the 'OA' of "8.25%" isn't even correct if the question had asked us to round to two decimal places. But a real GMAT question like this would always indicate that it's asking for an approximate answer rather than an exact one, so test takers know they shouldn't actually be calculating the value of 1.02^4.
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