What does Rs. 250 amount to in 2 years with compound interest at the rate of 4% per annum in the first year and 8% per annum in the second year?

Answer

To find out how much Rs. 250 amounts to in 2 years with compound interest at different rates for each year, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal and Rates**:
- Principal (P) = Rs. 250
- Rate for the first year (R1) = 4% per annum
- Rate for the second year (R2) = 8% per annum

2. **Convert the Rates into Decimal Form**:
- R1 = 4/100 = 0.04
- R2 = 8/100 = 0.08

3. **Use the Compound Interest Formula**:
When different rates are applied in different years, the formula for the amount (A) after n years is:
\[ A = P \times (1 + R1) \times (1 + R2) \]

4. **Substitute the Values into the Formula**:
\[ A = 250 \times (1 + 0.04) \times (1 + 0.08) \]

5. **Calculate Each Component**:
- Calculate \(1 + R1\):
\[ 1 + 0.04 = 1.04 \]
- Calculate \(1 + R2\):
\[ 1 + 0.08 = 1.08 \]

6. **Multiply the Components**:
\[ A = 250 \times 1.04 \times 1.08 \]

7. **Calculate the Product**:
- First, calculate \(1.04 \times 1.08\):
\[ 1.04 \times 1.08 = 1.1232 \]
- Now, multiply by the principal:
\[ A = 250 \times 1.1232 = 280.8 \]

8. **Final Amount**:
The amount after 2 years is Rs. 280.8.

### Final Answer:
**Rs. 280.8**