A man borrowed some money and agreed to payoff paying 3150 at the end of the 1st year and ₹4410 at the end of the 2nd year. if the rate of compound interest is 5% per annum, then the sum is.

Options

A. ₹5,000
B. ₹6,500
C. ₹ 7,000
D. ₹9,200

Answer

To solve the problem, we need to find the principal amount (P) that was borrowed, given that the man paid back ₹3150 at the end of the first year and ₹4410 at the end of the second year with a compound interest rate of 5% per annum.

### Step-by-Step Solution:

1. **Understanding the Payments:**
- The man pays ₹3150 at the end of the first year.
- He pays ₹4410 at the end of the second year.

2. **Calculating the Present Value of the Payments:**
- The present value (PV) of the payment made at the end of the first year (₹3150) can be calculated using the formula:
\[ PV_1 = \frac{3150}{(1 + r)^1} \]
where \( r = \frac{5}{100} = 0.05 \).
\[ PV_1 = \frac{3150}{1.05} = 3000 \]

3. **Calculating the Present Value of the Second Payment:**
- The present value of the payment made at the end of the second year (₹4410) is calculated as:
\[ PV_2 = \frac{4410}{(1 + r)^2} \]
\[ PV_2 = \frac{4410}{(1.05)^2} = \frac{4410}{1.1025} \approx 4000 \]

4. **Calculating the Total Principal Amount:**
- Now, we add the present values of both payments to find the total principal amount (P):
\[ P = PV_1 + PV_2 = 3000 + 4000 = 7000 \]

5. **Conclusion:**
- Therefore, the total sum borrowed (the principal amount) is ₹7000.

### Final Answer:
The sum borrowed is ₹7000.