A sum of money invested at compound interest amounts in 3 years to ₹ 2400 and in 4 years to ₹ 2520. The interest rate per annum is

Options

A. 0.05
B. 0.06
C. 0.1
D. 0.12

Answer

To find the interest rate per annum for the given compound interest problem, we can follow these steps:

### Step 1: Understand the Problem
We know that the amount after 3 years is ₹2400 and after 4 years is ₹2520. We need to find the rate of interest per annum.

### Step 2: Set Up the Equations
Let the principal amount be \( P \) and the rate of interest be \( R\% \) per annum.

For the amount after 3 years:
\[ A_1 = P \left(1 + \frac{R}{100}\right)^3 = 2400 \quad \text{(Equation 1)} \]

For the amount after 4 years:
\[ A_2 = P \left(1 + \frac{R}{100}\right)^4 = 2520 \quad \text{(Equation 2)} \]

### Step 3: Divide the Two Equations
To eliminate \( P \), we can divide Equation 2 by Equation 1:
\[ \frac{P \left(1 + \frac{R}{100}\right)^4}{P \left(1 + \frac{R}{100}\right)^3} = \frac{2520}{2400} \]

This simplifies to:
\[ 1 + \frac{R}{100} = \frac{2520}{2400} \]

### Step 4: Calculate the Right Side
Now, calculate \( \frac{2520}{2400} \):
\[ \frac{2520}{2400} = 1.05 \]

### Step 5: Set Up the Equation for \( R \)
Now we have:
\[ 1 + \frac{R}{100} = 1.05 \]

Subtract 1 from both sides:
\[ \frac{R}{100} = 0.05 \]

### Step 6: Solve for \( R \)
Multiply both sides by 100 to find \( R \):
\[ R = 0.05 \times 100 = 5 \]

### Conclusion
The rate of interest per annum is \( R = 5\% \).

---