A man borrows ₹ 4000 at compound rate of 15% interest. At the end of each year he pays back ₹ 1500. How much additional amount should he pay at the end of the third year to clear all his dues:

Correct option is A

Given:

1. Principal borrowed = ₹4000.
2. Compound interest rate = 15% per year.
3. Yearly repayment = ₹1500.
4. We need to calculate the additional amount to clear all dues at the end of the third year.

Formula Used:

1. Compound Interest Formula:

$$A = P \times (1 + r)^n$$​​

where:
- A = Total amount after n years,
- P = Principal amount,
- r = Rate of interest (in decimal),
- n = Number of years.

2. Outstanding balance after each year:

$$\text{Outstanding Balance} = \text{Remaining Principal} + \text{Accrued Interest}$$​​

Solution:

1. **Year 1:**
- At the end of the first year, the total amount including interest:

$$A_1 = 4000 \times (1 + 0.15) = 4000 \times 1.15 = 4600 \, \text{₹}$$​​

- After repaying ₹1500:

$$\text{Outstanding balance after Year 1} = 4600 - 1500 = 3100 \, \text{₹}$$​​

2. **Year 2:**
- At the end of the second year, interest is added to the remaining balance:

$$A_2 = 3100 \times (1 + 0.15) = 3100 \times 1.15 = 3565 \, \text{₹}$$​​

- After repaying ₹1500:

$$\text{Outstanding balance after Year 2} = 3565 - 1500 = 2065 \, \text{₹}$$​​

3. **Year 3:**
- At the end of the third year, interest is added to the remaining balance:

$$A_3 = 2065 \times (1 + 0.15) = 2065 \times 1.15 = 2374.75 \, \text{₹}$$​​

- No additional repayment has been made for the third year, so the entire amount is due.

Final Answer:

The additional amount to be paid at the end of the third year to clear all dues is ₹2374.75.