The interest on Rs 24,000 in 2 years compounded annually when the rates are 8% p.a. and 10% p.a. for two successive years is:

Options

A. Rs 3,994
B. Rs 4,512
C. Rs 5040
D. Rs 5866

Answer

To solve the problem of calculating the compound interest on Rs. 24,000 over 2 years with different interest rates for each year, follow these steps:

### Step 1: Calculate the interest for the first year at 8% p.a.
- **Formula for Interest**:
\[ \text{Interest} = \text{Principal} \times \frac{\text{Rate}}{100} \]
- **Calculation**:
\[ \text{Interest for Year 1} = 24000 \times \frac{8}{100} = 24000 \times 0.08 = 1920 \]

### Step 2: Calculate the new principal for the second year.
- **New Principal**:
\[ \text{New Principal} = \text{Original Principal} + \text{Interest for Year 1} \]
- **Calculation**:
\[ \text{New Principal} = 24000 + 1920 = 25840 \]

### Step 3: Calculate the interest for the second year at 10% p.a.
- **Calculation**:
\[ \text{Interest for Year 2} = 25840 \times \frac{10}{100} = 25840 \times 0.10 = 2584 \]

### Step 4: Calculate the total interest earned over the two years.
- **Total Interest**:
\[ \text{Total Interest} = \text{Interest for Year 1} + \text{Interest for Year 2} \]
- **Calculation**:
\[ \text{Total Interest} = 1920 + 2584 = 4504 \]

### Final Result:
The total interest earned on Rs. 24,000 over 2 years, compounded annually at rates of 8% and 10%, is **Rs. 4504**.

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