Simple and Compound Interest

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tanyasethi: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Mon Jul 11, 2011 1:13 pmFollowed by: 1 member

by tanyasethi » Fri Jul 15, 2011 2:38 am

$1200 is invested at a given interest rate for two years. The difference between the simple 2-year non-compounded return at the end of the two years and an annually compounded return is $132. What is the interest rate?

A. 10%

B. 11%

C. 12%

D. 13%

E. 14%

The correct answer is A
Please explain how we can get to the answer.

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Source: Beat The GMAT — Problem Solving | Fri Jul 15, 2011 2:38 am

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Fri Jul 15, 2011 2:55 am

R is interest rate
simple 2-year non-compunded return 1,200*R*2
compounded rate, 2 years (1,200+1,200*R)*R

difference ==> (1,200*R + 1,200*R^2) - 2,400*R=132

1,200R^2-1,200*R-132=0
R=(1,200-root{Discriminant} )/2,400
Discriminant D=1,200^2 -4*1,200*(-132)=1,440^2

(1,200-1,440)/2,400=-0.1 and R=|-0.1| or 0.1=10%

tanyasethi wrote:$1200 is invested at a given interest rate for two years. The difference between the simple 2-year non-compounded return at the end of the two years and an annually compounded return is $132. What is the interest rate?

A. 10%

B. 11%

C. 12%

D. 13%

E. 14%
The correct answer is A
Please explain how we can get to the answer.

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