If the rate of interest of Rs. 5000 is 10% per annum for the first 2 yr and `15%` for the next 2 yr is given, then the compound interest is

Options

A. Rs. 1680
B. Rs. 3001
C. Rs. 4100
D. Rs. 3750

Answer

To solve the problem of finding the compound interest on Rs. 5000 with different interest rates over 4 years, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal and Interest Rates:**
- Principal (P) = Rs. 5000
- Rate for the first 2 years (R1) = 10% per annum
- Rate for the next 2 years (R2) = 15% per annum

2. **Calculate the Amount after the First 2 Years:**
- Use the compound interest formula:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
- For the first 2 years:
\[ A_1 = 5000 \left(1 + \frac{10}{100}\right)^2 = 5000 \left(1 + 0.1\right)^2 = 5000 \times (1.1)^2 \]
- Calculate \( (1.1)^2 \):
\[ (1.1)^2 = 1.21 \]
- Now calculate \( A_1 \):
\[ A_1 = 5000 \times 1.21 = 6050 \]

3. **Calculate the Amount after the Next 2 Years:**
- Now, use the amount from the first 2 years as the principal for the next 2 years:
\[ A_2 = 6050 \left(1 + \frac{15}{100}\right)^2 = 6050 \left(1 + 0.15\right)^2 = 6050 \times (1.15)^2 \]
- Calculate \( (1.15)^2 \):
\[ (1.15)^2 = 1.3225 \]
- Now calculate \( A_2 \):
\[ A_2 = 6050 \times 1.3225 = 8001.125 \]

4. **Calculate the Compound Interest:**
- The compound interest (CI) is given by:
\[ CI = A - P \]
- Substitute the values:
\[ CI = 8001.125 - 5000 = 3001.125 \]

5. **Final Result:**
- The compound interest after 4 years is approximately Rs. 3001.125.

### Conclusion:
The compound interest on Rs. 5000 at 10% for the first 2 years and 15% for the next 2 years is approximately Rs. 3001.