Problem Solving

$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%

10% simple : 120+120 = simple 2-year non-compounded return at the end of the two years = 240

Using A:10% compound: Principal = 1200(1.1)^2 = 1452 (252)

Using C: 1200(1.12)^2 = 1506 (306 - 144*2)

Assumption: 252-120 = 132.. I got 10% but I read the question wrong or is there a mistake with question.

let i be interest
CI accumulated for two years = 1200(1+i)^2 - 1200
SI for two years = 1200*i*2
difference = 132
1200(1+i)^2-1200 -1200*i*2= 132
1200(i^2) = 132
i^2 = 11/100
i = root(11)/10
i as % = 10root(11)

I think choices are not correct.

user123321

The answer choices are correct

Correct answer is [spoiler]A-10%[/spoiler] as per Grockit GMAT

user123321 wrote:let i be interest
CI accumulated for two years = 1200(1+i)^2 - 1200
SI for two years = 1200*i*2
difference = 132
1200(1+i)^2-1200 -1200*i*2= 132
1200(i^2) = 132
i^2 = 11/100
i = root(11)/10
i as % = 10root(11)

I think choices are not correct.

user123321

karthikpandian19 wrote:The answer choices are correct

Correct answer is [spoiler]A-10%[/spoiler] as per Grockit GMAT

user123321 wrote:let i be interest
CI accumulated for two years = 1200(1+i)^2 - 1200
SI for two years = 1200*i*2
difference = 132
1200(1+i)^2-1200 -1200*i*2= 132
1200(i^2) = 132
i^2 = 11/100
i = root(11)/10
i as % = 10root(11)

I think choices are not correct.

user123321

It seems that the Question is not perfectly phrased. Is it the same Question wording as in Grockit GMAT??

Now As Karthik Says the answer is 10%, i feel that question needs to be rephrased. It should be

Difference between the SI added once in 2 years and CI compounded annually then According the the Question

SI would be 120 in 2 years as Interest would be added once in 2 years.
CI would be 120 + 132 ( first and second year ) componded annually.

CI-SI =132?? Therefore [spoiler]A ( 10% )[/spoiler]