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%

I found this question from GROCKIT and please find the explanation below:

Let r be the multiplier, so that if the interest rate was 7%, r would be 1.07.

Then the final value computed with simple interest would be 1200r, while the value with the annually compounded rate would be 1200r2.

We are given that the difference between these two is $132. Since the compounded sum will be greater, we can set up the following equation:

1200r2 - 1200r = 132.

Simplifying this equation, we can start by dividing by 12:
100r2 - 100r = 11. Now divide by 100...

r2 - r - .11 = 0

We can solve this equation using the quadratic formula:

a = 1
b = -1
c = -0.11


{1.1, -.1) We need the positive solution, 1.1, giving us the rate of 10%.

Anurag@Gurome wrote:

karthikpandian19 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%

Principal = $1200
Let the interest rate is R.
Simple 2-year non-compounded return at the end of the two years = 1200 + (1200 * R * 2) = 1200 + 2400R

Compounded rate of interest in 2 years = 1200(1 + R)²

Difference = 1200(1 + R)² - (1200 + 2400R) = 132
1200(R² + 2R + 1) - 1200 - 2400R = 132
1200R² = 132
R² = 132/1200 implies R ≈ 0.33, which implies rate ≈ 33%, which is none of the options and normally the GMAT answers are not in fractions.

Can anyone brief about this explanation?

karthikpandian19 wrote:I found this question from GROCKIT and please find the explanation below:

Let r be the multiplier, so that if the interest rate was 7%, r would be 1.07.

Then the final value computed with simple interest would be 1200r, while the value with the annually compounded rate would be 1200r2.

We are given that the difference between these two is $132. Since the compounded sum will be greater, we can set up the following equation:

1200r2 - 1200r = 132.

Simplifying this equation, we can start by dividing by 12:
100r2 - 100r = 11. Now divide by 100...

r2 - r - .11 = 0

We can solve this equation using the quadratic formula:

a = 1
b = -1
c = -0.11


{1.1, -.1) We need the positive solution, 1.1, giving us the rate of 10%.

Anurag@Gurome wrote:

karthikpandian19 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%

Principal = $1200
Let the interest rate is R.
Simple 2-year non-compounded return at the end of the two years = 1200 + (1200 * R * 2) = 1200 + 2400R

Compounded rate of interest in 2 years = 1200(1 + R)²

Difference = 1200(1 + R)² - (1200 + 2400R) = 132
1200(R² + 2R + 1) - 1200 - 2400R = 132
1200R² = 132
R² = 132/1200 implies R ≈ 0.33, which implies rate ≈ 33%, which is none of the options and normally the GMAT answers are not in fractions.

Differnece of C.I and S.I for 2 yrs = P(r/100)^2=132

Can you elaborate?

ArunangsuSahu wrote:Differnece of C.I and S.I for 2 yrs = P(r/100)^2=132

I agree with Anurag's answer:

So, the difference in the returns is the difference in amount of interest earned by the 2 investments.

Simple Interest -- 1200 * 2 * I
Compound Interest -- 1200[1 + I ]^2 - 1200 ==> 1200[I^2 + 2I]

Difference between the two interest amounts is:
1200[I^2], which is 132. Recall, that in the final step, we should treat I as %.

So, (I/100)^2 = 132/1200, which boils down to 33% approx:

I've noticed that Grockit has had quite a few errors in their quant section. Probably one of those questions?