If some amount becomes 2400 in 3 years and 2520 in 4 years then find the rate of interest?

Options

A. `7%`
B. `6%`
C. `4.5%`
D. `5%`

Answer

To find the rate of interest given that an amount becomes Rs. 2400 in 3 years and Rs. 2520 in 4 years, we can follow these steps:

### Step 1: Identify the amounts
- Amount after 3 years (A3) = Rs. 2400
- Amount after 4 years (A4) = Rs. 2520

### Step 2: Calculate the interest for the 4th year
The interest earned in the 4th year can be calculated as:
\[ \text{Interest for 4th year} = A4 - A3 \]
\[ \text{Interest for 4th year} = 2520 - 2400 = 120 \]

### Step 3: Use the formula for rate of interest
The formula for calculating the rate of interest (R) is:
\[ R = \left( \frac{\text{Interest}}{\text{Principal}} \right) \times 100 \]

Here, the principal amount (A3) is Rs. 2400, and the interest for the 4th year is Rs. 120.

### Step 4: Substitute the values into the formula
\[ R = \left( \frac{120}{2400} \right) \times 100 \]

### Step 5: Simplify the calculation
\[ R = \left( \frac{120}{2400} \right) \times 100 = \left( \frac{1}{20} \right) \times 100 = 5 \]

### Conclusion
The rate of interest is **5%**.

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