A man invests रु 5,600 at 14% per annum compound interest for 2 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:**
\[ \text{Interest} = \frac{P \times R \times T}{100} \]

Where:
- \( P = 5600 \) (Principal amount)
- \( R = 14 \) (Rate of interest)
- \( T = 1 \) (Time in years)

**Calculation:**
\[ \text{Interest} = \frac{5600 \times 14 \times 1}{100} \]
\[ \text{Interest} = \frac{78400}{100} \]
\[ \text{Interest} = 784 \]

**Result:**
The interest for the first year is **रु 784**.

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

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

**Calculation:**
\[ \text{Amount} = 5600 + 784 \]
\[ \text{Amount} = 6384 \]

**Result:**
The amount at the end of the first year is **रु 6384**.

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

**New Principal for the second year:**
The principal for the second year is the amount at the end of the first year, which is **रु 6384**.

**Formula:**
\[ \text{Interest} = \frac{P \times R \times T}{100} \]

Where:
- \( P = 6384 \) (New Principal amount)
- \( R = 14 \) (Rate of interest)
- \( T = 1 \) (Time in years)

**Calculation:**
\[ \text{Interest} = \frac{6384 \times 14 \times 1}{100} \]
\[ \text{Interest} = \frac{89456}{100} \]
\[ \text{Interest} = 894.56 \]

**Rounding to the nearest rupee:**
The interest for the second year is approximately **रु 895**.

### Final Results:
(i) The interest for the first year is **रु 784**.
(ii) The amount at the end of the first year is **रु 6384**.
(iii) The interest for the second year, correct to the nearest rupee, is **रु 895**.

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