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 principal for the second year.

Answer

To find the principal for the second year after Peter repays Rs. 8,000 at the end of the first year, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Principal and Rate of Interest:**
- Peter borrows Rs. 12,000 for 2 years at a rate of 10% per annum.

2. **Calculate the Interest for the First Year:**
- Use the formula for calculating simple interest:
\[ \text{Interest} = \frac{P \times R \times T}{100} \]
- Here, \( P = 12000 \), \( R = 10 \), and \( T = 1 \) (for the first year).
- Plugging in the values:
\[ \text{Interest} = \frac{12000 \times 10 \times 1}{100} = 1200 \]

3. **Calculate the Total Amount at the End of the First Year:**
- Total Amount = Principal + Interest
- Total Amount = Rs. 12,000 + Rs. 1,200 = Rs. 13,200

4. **Determine the Amount Remaining After Repayment:**
- Peter repays Rs. 8,000 at the end of the first year.
- Remaining Amount = Total Amount - Repayment
- Remaining Amount = Rs. 13,200 - Rs. 8,000 = Rs. 5,200

5. **Conclusion: Find the Principal for the Second Year:**
- The principal for the second year is the remaining amount after the repayment.
- Therefore, the principal for the second year is Rs. 5,200.

### Final Answer:
The principal for the second year is Rs. 5,200.

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