a man borrowed a certain sum and agrees to repay it by paying rs 4000 at the end of first year and rs 7700 at the end of second year. If the rate of compound interest compounded annually is 10% per annum, then find the sum borrowed?

To find the sum borrowed, let's denote the borrowed sum as \( P \). The borrower is making two payments: Rs 4000 at the end of the first year and Rs 7700 at the end of the second year, with compound interest compounded annually at 10%.

The total borrowed amount will have grown by the time the payments are made, so we can calculate the present value of each payment as follows.

### Step 1: The formula for compound interest:
The amount \( A \) after \( n \) years at a rate of interest \( r \) is given by:
\[
A = P(1 + \frac{r}{100})^n
\]
Where:
- \( P \) is the present value (sum borrowed),
- \( r \) is the rate of interest (10% in this case),
- \( n \) is the number of years.

### Step 2: Breaking down the repayment schedule:
1. **First Payment (Rs 4000 at the end of the first year)**:
   - The present value of this payment (i.e., what it would be worth today) is:
   \[
   \text{Present value of Rs 4000} = \frac{4000}{(1 + \frac{10}{100})^1} = \frac{4000}{1.1} = 3636.36 \, \text{(approx)}
   \]

2. **Second Payment (Rs 7700 at the end of the second year)**:
   - The present value of this payment (i.e., what it would be worth today) is:
   \[
   \text{Present value of Rs 7700} = \frac{7700}{(1 + \frac{10}{100})^2} = \frac{7700}{1.1^2} = \frac{7700}{1.21} = 6363.64 \, \text{(approx)}
   \]

### Step 3: Total borrowed sum
The total sum borrowed is the sum of the present values of both payments:
\[
P = 3636.36 + 6363.64 = 10000
\]

Thus, the sum borrowed is **Rs 10,000**.

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Would you like more details on any part of the solution, or do you have any other questions?

Here are some related questions:
1. What is the future value of Rs 10,000 after 2 years at 10% interest?
2. How does compound interest differ from simple interest in such scenarios?
3. What if the borrower made an additional payment after the second year? How would the calculation change?
4. How is the present value formula derived for compound interest?
5. What happens if the interest rate changes after the first year?

**Tip**: When dealing with compound interest, always note the compounding period (annually, semi-annually, etc.) as it affects the final calculations.

A man borrowed a certain sum and agrees to repay it by paying Rs 4000 at the end of the first year and Rs 7700 at the end of the second year. If the rate of compound interest compounded annually is 10% per annum, then find the sum borrowed.

Learn how to calculate the sum borrowed when a man agrees to repay Rs 4000 at the end of the first year and Rs 7700 at the end of the second year with compound interest compounded annually at 10%. This problem covers concepts of compound interest and present value, suitable for students in Grades 10-12.

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