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₹ 1,000 is borrowed at 10% per annum compound interest. If ₹ 300 is repaid at the end of each year, what is the amount of loan outstanding at the end of the 2nd year?



Answer :

GinnyAnswer
Let's solve this problem step-by-step:

### Initial Details:
- Principal Amount: ₹ 1,000
- Interest Rate: 10% per annum (compound interest)
- Annual Repayment: ₹ 300
- Time Period: 2 years

### First Year:

1. Initial Principal (at the start of the year): ₹ 1,000
2. Interest for the First Year:
- The interest is calculated on the initial principal amount.
- \( \text{Interest} = 1{,}000 \times \frac{10}{100} = 1,000 \times 0.10 = ₹ 100 \)
3. Total Amount at the End of First Year (before repayment):
- This is the sum of the principal plus the interest added.
- \( \text{Total Amount} = 1{,}000 + 100 = ₹ 1{,}100 \)
4. Repayment at the End of First Year:
- Subtract the repayment amount from the total amount.
- \( \text{Amount after Repayment} = 1{,}100 - 300 = ₹ 800 \)

### Second Year:

1. Principal Amount at the Start of the Second Year: ₹ 800
2. Interest for the Second Year:
- The interest is now calculated on the remaining principal amount after the first year's repayment.
- \( \text{Interest} = 800 \times \frac{10}{100} = 800 \times 0.10 = ₹ 80 \)
3. Total Amount at the End of Second Year (before repayment):
- This is the sum of the new principal plus the interest added.
- \( \text{Total Amount} = 800 + 80 = ₹ 880 \)
4. Repayment at the End of Second Year:
- Subtract the repayment amount from the total amount.
- \( \text{Amount after Repayment} = 880 - 300 = ₹ 580 \)

### Conclusion:

The amount of loan outstanding at the end of the 2nd year is ₹ 580.

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