Question

If Rs. 600 amounts to Rs. 683.20 in two years compounded annually, find the rate of interest per annum.

• A. 8
• B. 10
• C. 9
• D. 7
• E.

Hint:

For compound interest, use the formula: \[ A = P \left(1 + \frac{r}{100}\right)^t. \] and solve for \( r \).

Answer 1

The Correct Option is D

Step 1: Apply the compound interest formula: \[ A = P \left(1 + \frac{r}{100}\right)^t \] where \( A = 683.20 \), \( P = 600 \), \( t = 2 \), and \( r \) is the rate of interest. Step 2: Substituting the given values: \[ 683.20 = 600 \left(1 + \frac{r}{100}\right)^2. \] Step 3: Simplifying the equation: \[ \frac{683.20}{600} = \left(1 + \frac{r}{100}\right)^2 \] \[ 1.13867 = \left(1 + \frac{r}{100}\right)^2. \] Step 4: Taking the square root on both sides: \[ 1 + \frac{r}{100} = \sqrt{1.13867} \] \[ 1 + \frac{r}{100} = 1.0667. \] Step 5: Solving for \( r \): \[ \frac{r}{100} = 0.0667 \] \[ r = 6.67. \] Thus, the rate of interest per annum is approximately **7\%**.