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Simple one on Simple and Compound interest

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Simple one on Simple and Compound interest

by knight247 » Thu Jun 30, 2011 1:07 am
X invested some amount for 2 years at simple interest. Y invested the same amount for the same period at the same interest rate per annum but at compound interest with annual compounding. At the end of 2 years, apart from the amount invested, X received $200 as interest and Y received $220 as interest. What was the rate of interest in percent per annum?

(A)13%
(B)20%
(C)22%
(D)15%
(E)10%

The answer as per my calculation is [spoiler](B)[/spoiler]. Don't have an official OA. Detailed explanations would be appreciated. Than
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by GMATGuruNY » Thu Jun 30, 2011 1:47 am
knight247 wrote:X invested some amount for 2 years at simple interest. Y invested the same amount for the same period at the same interest rate per annum but at compound interest with annual compounding. At the end of 2 years, apart from the amount invested, X received $200 as interest and Y received $220 as interest. What was the rate of interest in percent per annum?

(A)13%
(B)20%
(C)22%
(D)15%
(E)10%

The answer as per my calculation is [spoiler](B)[/spoiler]. Don't have an official OA. Detailed explanations would be appreciated. Than
We can plug in the answers, which represent the annual interest rate.
Since the amounts earned by X and Y are both multiples of 10, the correct answer also is likely a multiple of 10.

Answer choice B: 20% annual interest
For 20% interest to earn for X 200/2=100 per year, X must invest 500.
Thus, Y also invests 500.
Compounded interest for Y:
First year = .2*500 = 100.
New balance = 500+100 = 600.
Second year = .2*600 = 120.
Total interest earned = 100+120 = 220.
Success!

The correct answer is B.
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by Geva@EconomistGMAT » Thu Jun 30, 2011 2:26 am
Simple interest means that the interest is only taken from the original Principal. It also means that the interest is the same constant figure every year. If the simple interest account made $200 in two years, then each year the interest was $100.

Let's look at the compound interest account. After a single year, there's no difference between the two accounts, since the interest is compounded annually (i.e. only once a year). After the second year, the compound account has $20 more. That difference between simple and compound is the "interest on the interest": the extra $20 are taken as the interest on the $100 interest accrued in the first year.

All this brings us to the interest rate of 20% ($20 on $100) - answer choice B.
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