What will be the amount if a sum of Rs. 5000 is placed at compound interest for 3 years while rate of interest for the first, second and third years is 2%, 3% and 4% respectively?

Answer

To find the amount when a sum of Rs. 5000 is placed at compound interest for 3 years with varying rates of interest (2% for the first year, 3% for the second year, and 4% for the third year), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal and Rates**:
- Principal (P) = Rs. 5000
- Rate for Year 1 (r1) = 2%
- Rate for Year 2 (r2) = 3%
- Rate for Year 3 (r3) = 4%

2. **Convert Rates to Decimal**:
- Convert the percentage rates to decimal for calculation:
- r1 = 2/100 = 0.02
- r2 = 3/100 = 0.03
- r3 = 4/100 = 0.04

3. **Calculate the Amount After Each Year**:
- **After Year 1**:
\[ A_1 = P \times (1 + r1) = 5000 \times (1 + 0.02) = 5000 \times 1.02 = 5100 \]
- **After Year 2**:
\[ A_2 = A_1 \times (1 + r2) = 5100 \times (1 + 0.03) = 5100 \times 1.03 = 5253 \]
- **After Year 3**:
\[ A_3 = A_2 \times (1 + r3) = 5253 \times (1 + 0.04) = 5253 \times 1.04 = 5460.12 \]

4. **Final Amount**:
- The total amount after 3 years is Rs. 5460.12.

### Final Answer:
The amount after 3 years will be Rs. 5460.12.

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