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%

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On the first of the year, James invested x dollars at Proudstar bank

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Bunuel

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darsh.shah

Hi Mike, Is there any way to arrive at numbers like y = x*(1.02)^4 = (1.08243216)*x within 2 minutes without any calculator? Because this will take some more time to calculate and it would be difficult to estimate if options are near.

mikemcgarry

Hi, there. I'm happy to help with this.

Essentially, this question is asking for the effective interest rate.

So, every increase of 2% means we multiply x by the multiplier 1.02. The initial amount x gets multiplied by this multiply four times, one for each quarter, so . . .

y = x*(1.02)^4 = (1.08243216)*x ====> effective interest = 8.2432%

That's how you'd get the exact answer with a calculator, but of course you don't have a calculator available on GMAT PS questions. Think about it this way. With simple interest, 2% a quarter would add up to 8% annual. With compound interest, where you get interest on your interest, you will do a little better than you would with simple interest, so the answer should be something slightly above 8%. That leads us to . . .

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Answer = D

Does that make sense? Please let me know if you have any additional questions on what I've said there.

Mike

If you read the thread carefully enough, you'll see that you don't actually need to calculate exactly.