Martina invested $1000 for a period of 17 years in a bank that paid

Question

Martina invested $1000 for a period of 17 years in a bank that paid variable rates of interest. For the first 2 years, the bank paid an annual interest rate of x percent compounded annually and for the next 5 years, the bank paid a simple interest rate of 12 percent per annum on the compounded amount at the end of the second year. If for the remaining years, Martina earned a total simple interest of $1694 on the compounded amount at the end of the second year, at a rate of 14 percent per annum, by approximately what percentage of the invested amount was the total simple interest earned greater than the compound interest earned?

A. 208%
B. 221%
C. 229%
D. 242%
E. Cannot be determined

IanStewart · Answer

I think the best answer to this question is "who cares", because you'll never see anything even vaguely like this on the GMAT. But if we want to solve it:

- simple interest is the same each year; it's just a fixed percentage of the starting capital. So if the person earned $1694 in simple interest over 10 years, she earned $169.4 in interest each year. If that's 14% of the starting capital C, then 0.14C = 169.4, and solving we find C = 1210. That, according to the wording of the question, is the value of the investment after two years.

- since the only compound interest accrues in the first two years, the total amount of compound interest is thus $210

- we also have five years of simple interest on the $1210 amount, at 12% each year. Since it's simple interest, that's the same as earning 60% once, so 0.6*1210 = $726 is the amount of interest earned at 12%.

- adding the simple interest at 12% to the simple interest at 14%, the total simple interest was $1694 + $726 = $2420

So the total simple interest earned was 2420 - 210 = 2210 greater than the compound interest earned. Since we want to express that difference as a percentage of the initial investment, we must divide by 1000, to get 2.21, and multiply by 100%, so the answer is 221%.

Martina invested $1000 for a period of 17 years in a bank that paid

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