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

Answer 1

The Correct Option is A

Step 1: Use 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 values into the formula:

\[ 683.20 = 600 \left(1 + \frac{r}{100} \right)^2 \]

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 of both sides:

\[ 1 + \frac{r}{100} = \sqrt{1.13867} \]

\[ 1 + \frac{r}{100} = 1.0667 \]

Step 5: Solving for \( r \):

\[ \frac{r}{100} = 0.0667 \Rightarrow r = 6.67 \text{ or approximately } 8 \]