interest rates

$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?

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, -0.1) We need the positive solution, 1.1, giving us the rate of 10%.

Posted Tue Jul 19, 2011 5:47 am
finance 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?

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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.

AN24 wrote:

Posted Tue Jul 19, 2011 5:47 am
finance 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?

- 10
- 11
- 12
- 13
- 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.

Hi Anurag,

Amount= P+I
for SI, we r finding the total amount (1200+2400R)
but for CI, we are only finding the interest [1200(1+R)^2]
the amount for CI implied over 2 yrs should be = 1200+[1200(1+R)^2]

Following this, i get r= 10 rt(10)