A man borrows Rs. 4000 from a bank at `7(1)/(2)%` compound interest. At the end of every year he pays Rs. 1500 as part repayment of loan and interest. How much does he still owe to the bank after three such installments?

Answer

To solve the problem step by step, we will calculate the amount owed after each year considering the compound interest and the repayments made.

### Step 1: Calculate the amount after the first year
- **Principal (P)** = Rs. 4000
- **Rate of interest (R)** = 7.5% = 0.075 (as a decimal)
- **Amount after 1 year (A)** = P × (1 + R)

\[ A = 4000 \times (1 + 0.075) = 4000 \times 1.075 = 4300 \]

After the first year, the total amount owed is Rs. 4300.

### Step 2: Repayment after the first year
- **Repayment** = Rs. 1500
- **Remaining amount after repayment** = A - Repayment

\[ Remaining = 4300 - 1500 = 2800 \]

### Step 3: Calculate the amount after the second year
- **New Principal (P)** = Rs. 2800
- **Amount after 2 years (A)** = P × (1 + R)

\[ A = 2800 \times (1 + 0.075) = 2800 \times 1.075 = 3001 \]

After the second year, the total amount owed is Rs. 3001.

### Step 4: Repayment after the second year
- **Repayment** = Rs. 1500
- **Remaining amount after repayment** = A - Repayment

\[ Remaining = 3001 - 1500 = 1501 \]

### Step 5: Calculate the amount after the third year
- **New Principal (P)** = Rs. 1501
- **Amount after 3 years (A)** = P × (1 + R)

\[ A = 1501 \times (1 + 0.075) = 1501 \times 1.075 = 1613.075 \]

After the third year, the total amount owed is Rs. 1613.075.

### Step 6: Repayment after the third year
- **Repayment** = Rs. 1500
- **Remaining amount after repayment** = A - Repayment

\[ Remaining = 1613.075 - 1500 = 113.075 \]

### Final Answer
After three installments, the man still owes Rs. 113.075 to the bank.

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