Calculate the compound interest for the second year on Rs. 4,000 invested for 3 years at 10% per annum.

Answer

To calculate the compound interest for the second year on Rs. 4,000 invested for 3 years at 10% per annum, we can follow these steps:

### Step 1: Calculate the amount at the end of the first year.
- **Formula**: \( A = P \left(1 + \frac{r}{100}\right)^n \)
- **Where**:
- \( P = 4000 \) (Principal)
- \( r = 10\% \) (Rate of interest)
- \( n = 1 \) (Time in years)

**Calculation**:
\[ A_1 = 4000 \left(1 + \frac{10}{100}\right)^1 \]
\[ A_1 = 4000 \left(1 + 0.10\right) \]
\[ A_1 = 4000 \times 1.10 = 4400 \]

### Step 2: Calculate the amount at the end of the second year using the amount from the first year as the principal.
- **New Principal**: \( P = 4400 \)
- **Rate of interest**: \( r = 10\% \)
- **Time**: \( n = 1 \)

**Calculation**:
\[ A_2 = 4400 \left(1 + \frac{10}{100}\right)^1 \]
\[ A_2 = 4400 \left(1 + 0.10\right) \]
\[ A_2 = 4400 \times 1.10 = 4840 \]

### Step 3: Calculate the compound interest for the second year.
- **Compound Interest for the second year**:
\[ \text{CI for second year} = A_2 - A_1 \]
\[ \text{CI for second year} = 4840 - 4400 = 440 \]

### Final Answer:
The compound interest for the second year is **Rs. 440**.

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