A sum of रु 13,500 is invested at 16% per annum compound interest for 5 years. Calculate :
(i) the interest for the first year.
(ii) the amount at the end of the first year.
(iii) the interest for the second year, correct to the nearest rupee.

Explanation

To solve the problem step by step, we will calculate the interest for the first year, the amount at the end of the first year, and the interest for the second year.

### Step 1: Calculate the interest for the first year.

**Formula for Compound Interest for the first year:**
\[ \text{Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (initial investment)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

**Given:**
- \( P = 13,500 \)
- \( R = 16\% \)
- \( T = 1 \) year

**Calculation:**
\[ \text{Interest} = \frac{13,500 \times 16 \times 1}{100} = \frac{216,000}{100} = 2,160 \]

**Interest for the first year = रु 2,160.**

### Step 2: Calculate the amount at the end of the first year.

**Formula for Amount:**
\[ \text{Amount} = P + \text{Interest} \]

**Calculation:**
\[ \text{Amount} = 13,500 + 2,160 = 15,660 \]

**Amount at the end of the first year = रु 15,660.**

### Step 3: Calculate the interest for the second year.

For the second year, the principal will be the amount at the end of the first year.

**New Principal (P) = 15,660.**

**Using the same formula for interest:**
\[ \text{Interest} = \frac{P \times R \times T}{100} \]

**Given:**
- \( P = 15,660 \)
- \( R = 16\% \)
- \( T = 1 \) year

**Calculation:**
\[ \text{Interest} = \frac{15,660 \times 16 \times 1}{100} = \frac{250,560}{100} = 2,505.60 \]

**Rounding to the nearest rupee:**
\[ \text{Interest for the second year} \approx 2,506 \]

**Interest for the second year = रु 2,506.**

### Summary of Results:
1. Interest for the first year = रु 2,160
2. Amount at the end of the first year = रु 15,660
3. Interest for the second year = रु 2,506

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