If a certain sum on compound interest becomes Rs. 2000 in 2 years and Rs. 2200 in 3 years, find rate of interest per annum

Answer

To solve the problem of finding the rate of interest per annum given that a certain sum on compound interest becomes Rs. 2000 in 2 years and Rs. 2200 in 3 years, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amounts:**
- Amount after 2 years (A2) = Rs. 2000
- Amount after 3 years (A3) = Rs. 2200

2. **Calculate the Interest for the 3rd Year:**
- The interest earned in the 3rd year can be calculated by subtracting the amount after 2 years from the amount after 3 years:
\[ \text{Interest for 3rd year} = A3 - A2 = 2200 - 2000 = Rs. 200 \]

3. **Determine the Principal for the 3rd Year:**
- The principal amount for the 3rd year is the amount after 2 years:
\[ \text{Principal (P)} = A2 = Rs. 2000 \]

4. **Use the Simple Interest Formula:**
- The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
- Here, SI = Rs. 200 (interest for the 3rd year), P = Rs. 2000, and T = 1 year.

5. **Substitute the Known Values:**
- Plugging in the values into the simple interest formula:
\[ 200 = \frac{2000 \times R \times 1}{100} \]

6. **Rearranging the Equation:**
- To isolate R, we can rearrange the equation:
\[ 200 = \frac{2000R}{100} \implies 200 = 20R \]

7. **Solve for R:**
- Dividing both sides by 20 gives:
\[ R = \frac{200}{20} = 10 \]

8. **Conclusion:**
- Therefore, the rate of interest per annum is:
\[ \text{Rate of Interest} = 10\% \]

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

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