A sum of money amounts to ₹4840 in 2 years and ₹5324 in 3 years at compound interest compounded annually. What is the rate of interest per annum?

Answer

To find the rate of interest per annum given that a sum of money amounts to ₹4840 in 2 years and ₹5324 in 3 years at compound interest compounded annually, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let \( P \) be the principal amount and \( R \) be the rate of interest per annum.

2. **Write the Amount Formulas**:
According to the compound interest formula, the amount \( A \) after \( n \) years is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
- For 2 years:
\[ A_2 = P \left(1 + \frac{R}{100}\right)^2 = 4840 \quad \text{(Equation 1)} \]
- For 3 years:
\[ A_3 = P \left(1 + \frac{R}{100}\right)^3 = 5324 \quad \text{(Equation 2)} \]

3. **Divide the Two Equations**:
To eliminate \( P \), divide Equation 2 by Equation 1:
\[ \frac{A_3}{A_2} = \frac{P \left(1 + \frac{R}{100}\right)^3}{P \left(1 + \frac{R}{100}\right)^2} \]
This simplifies to:
\[ \frac{5324}{4840} = 1 + \frac{R}{100} \]

4. **Calculate the Left Side**:
Calculate \( \frac{5324}{4840} \):
\[ \frac{5324}{4840} = 1.1 \]

5. **Set Up the Equation**:
Now we have:
\[ 1 + \frac{R}{100} = 1.1 \]

6. **Solve for \( R \)**:
Subtract 1 from both sides:
\[ \frac{R}{100} = 0.1 \]
Multiply both sides by 100:
\[ R = 10 \]

7. **Conclusion**:
The rate of interest per annum is \( R = 10\% \).