The approximate compound interest on Rs. 5000 for 4 yr of the rate of interest Is 10% per annum for the first two years and 15% for the next two years is
(a) ₹ 3001
(b) ₹ 2001
(c) ₹ 5001
(d) ₹ 3021

Options

A. ₹ 3001
B. ₹ 2001
C. ₹ 5001
D. ₹ 3021

Answer

To calculate the approximate compound interest on Rs. 5000 for 4 years with different rates of interest for the two periods, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Principal and Rates**:
- Principal (P) = Rs. 5000
- Rate for the first 2 years (r1) = 10%
- Rate for the next 2 years (r2) = 15%

2. **Calculate the Amount after the First 2 Years**:
- Use the compound interest formula for the first 2 years:
\[ A_1 = P \left(1 + \frac{r1}{100}\right)^n \]
- Here, \( n = 2 \) years, so:
\[ A_1 = 5000 \left(1 + \frac{10}{100}\right)^2 = 5000 \left(1.1\right)^2 \]
- 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:
\[ A_2 = A_1 \left(1 + \frac{r2}{100}\right)^n \]
- Here, \( n = 2 \) years and \( r2 = 15\% \):
\[ A_2 = 6050 \left(1 + \frac{15}{100}\right)^2 = 6050 \left(1.15\right)^2 \]
- Calculate \( (1.15)^2 \):
\[ (1.15)^2 = 1.3225 \]
- Now calculate \( A_2 \):
\[ A_2 = 6050 \times 1.3225 \approx 8001.125 \]

4. **Calculate the Compound Interest**:
- The compound interest (CI) is given by:
\[ CI = A_2 - P \]
- Substitute the values:
\[ CI = 8001.125 - 5000 = 3001.125 \]
- Rounding off gives us approximately Rs. 3001.

5. **Final Answer**:
- The approximate compound interest on Rs. 5000 for 4 years is Rs. 3001.