A sum of money invested at compound Interest amounts to `Rs. 800` in 3 years and to `Rs. 840`in 4 years. The rate of interest per annum is:

Options

A. `2(1)/2%`
B. `4%`
C. `5%`
D. `6(2)/3%`

Answer

To find the rate of interest per annum when a sum of money invested at compound interest amounts to Rs. 800 in 3 years and Rs. 840 in 4 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amounts:**
- Amount after 3 years (A1) = Rs. 800
- Amount after 4 years (A2) = Rs. 840

2. **Calculate the Interest Earned in the 4th Year:**
- The interest earned in the 4th year can be calculated as:
\[ \text{Interest in 4th year} = A2 - A1 = 840 - 800 = Rs. 40 \]

3. **Determine the Principal Amount at the End of 3 Years:**
- The amount after 3 years is Rs. 800, which is the principal plus the interest earned over the 3 years.

4. **Calculate the Rate of Interest:**
- The interest earned in the 4th year is Rs. 40, and this interest is calculated on the amount at the end of 3 years (Rs. 800).
- Using the formula for interest:
\[ \text{Rate} = \left( \frac{\text{Interest}}{\text{Principal}} \right) \times 100 \]
- Substituting the values:
\[ \text{Rate} = \left( \frac{40}{800} \right) \times 100 \]

5. **Simplify the Calculation:**
- Calculate:
\[ \text{Rate} = \left( \frac{1}{20} \right) \times 100 = 5\% \]

### Final Answer:
The rate of interest per annum is **5%**.

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