Peter borrows Rs. 12,000 for 2 years at 10% p.a. compound interest. He repays Rs. 8,000 at the end of first year. Find :
the amount to be paid at the end of second year, to clear the debt.

Answer

To solve the problem step by step, we will follow the process of calculating the compound interest and the repayments made by Peter.

### Step 1: Calculate the Interest for the First Year
We will use the formula for calculating simple interest:
\[ \text{Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P = 12,000 \) (the principal amount)
- \( R = 10 \) (the rate of interest)
- \( T = 1 \) (time in years)

Substituting the values:
\[ \text{Interest} = \frac{12,000 \times 10 \times 1}{100} = 1,200 \]

### Step 2: Calculate the Total Amount After the First Year
The total amount after one year is the sum of the principal and the interest:
\[ \text{Total Amount} = P + \text{Interest} = 12,000 + 1,200 = 13,200 \]

### Step 3: Calculate the Remaining Amount After Peter's Repayment
Peter repays Rs. 8,000 at the end of the first year. So, the remaining amount after repayment is:
\[ \text{Remaining Amount} = \text{Total Amount} - \text{Repayment} = 13,200 - 8,000 = 5,200 \]

### Step 4: Calculate the Interest for the Second Year
Now, we will calculate the interest for the second year using the remaining amount as the new principal:
\[ \text{Interest for Second Year} = \frac{P \times R \times T}{100} \]
Where:
- \( P = 5,200 \) (the new principal)
- \( R = 10 \) (the rate of interest)
- \( T = 1 \) (time in years)

Substituting the values:
\[ \text{Interest for Second Year} = \frac{5,200 \times 10 \times 1}{100} = 520 \]

### Step 5: Calculate the Total Amount to be Paid at the End of the Second Year
The total amount to be paid at the end of the second year is the sum of the remaining principal and the interest for the second year:
\[ \text{Total Amount at End of Second Year} = \text{Remaining Amount} + \text{Interest for Second Year} = 5,200 + 520 = 5,720 \]

### Final Answer
Peter will need to pay Rs. 5,720 at the end of the second year to clear his debt.

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