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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 1:35 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 Geva@EconomistGMAT » Thu Jun 30, 2011 2:46 am
B it is.

Since the compound interest is still compounded annually (once a year), after the first year there's no difference between the simple and compound interest - each will only accrue interest once.

It's after the second year that the difference manifests.

Simple interest is always taken from the Principal. It's the same fixed amount every year: if the simple account does $200 in two years, this means that he does $100 a year, flat.

Compound interest will accrue the same $100 interest on the principal, but will also accrue extra interest on the interest accrued in the first year. That's the source of the $20 difference between the two accounts: the $20 extra is the interest taken from the extra $100 the compound account accumulated in the first year.

A $20 interest on a $100 "principal" amounts to 20% interest - hence B.
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by amit2k9 » Thu Jun 30, 2011 3:02 am
let the simple interest for 2 year be
pr*2/100 = 200
pr = 10^4.

simple interest for 1 year = 100.
compound interest for 2 years = 220
thus simple interest for 2nd year = 220-100=120.
calculating for the 2nd year

(p+100)r*1/100 = 120
thus
pr+100r = 120*100 giving r= 20%

B it is.
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