A sum of money on compound interest amounts `Rs. 10648` in 3 years and `Rs. 9680` in 2 years. The rate of interest per annum is:

Options

A. `5%`
B. `10%`
C. `15%`
D. `20%`

Answer

To find the rate of interest per annum, we can use the formula for compound interest. We know the amounts after 2 years and 3 years, which will help us find the rate of interest.

### Step-by-Step Solution:

1. **Identify the amounts:**
- Amount after 2 years (A2) = Rs. 9,680
- Amount after 3 years (A3) = Rs. 10,648

2. **Use the formula for compound interest:**
The formula for the amount after 'n' years is given by:
\[ A = P(1 + r)^n \]
where:
- A = Amount after n years
- P = Principal amount (initial sum)
- r = Rate of interest per annum (in decimal)
- n = Number of years

3. **Set up the equations:**
From the amounts given, we can set up the following equations:
- For 2 years:
\[ A2 = P(1 + r)^2 \implies 9680 = P(1 + r)^2 \quad \text{(1)} \]
- For 3 years:
\[ A3 = P(1 + r)^3 \implies 10648 = P(1 + r)^3 \quad \text{(2)} \]

4. **Divide the two equations:**
To eliminate P, we can divide equation (2) by equation (1):
\[ \frac{A3}{A2} = \frac{P(1 + r)^3}{P(1 + r)^2} \]
This simplifies to:
\[ \frac{10648}{9680} = 1 + r \]

5. **Calculate the left side:**
Now, we calculate the left side:
\[ \frac{10648}{9680} = 1.1 \]

6. **Solve for r:**
Now we have:
\[ 1 + r = 1.1 \implies r = 1.1 - 1 = 0.1 \]
Converting this to a percentage:
\[ r = 0.1 \times 100 = 10\% \]

### Final Answer:
The rate of interest per annum is **10%**.