A man borrowed a sum of money and agrees to pay it off by paying Rs 43,200 at the end of the first year and Rs 34,992 at the end of the second year. If the rate of compound interest is 8% per annum, find the sum borrowed.

Answer

To find the sum borrowed by the man, we will calculate the present value of the payments made at the end of the first and second years using the compound interest formula.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Payment at the end of the first year (A1) = Rs 43,200
- Payment at the end of the second year (A2) = Rs 34,992
- Rate of interest (R) = 8% per annum

2. **Calculate the Present Value of the First Payment (P1):**
- The formula for the present value (PV) is:
\[ PV = \frac{A}{(1 + \frac{R}{100})^T} \]
- For the first payment (end of year 1):
- A1 = 43,200
- T1 = 1 year
- Substitute the values into the formula:
\[ P1 = \frac{43200}{(1 + \frac{8}{100})^1} = \frac{43200}{1.08} \]
- Calculate P1:
\[ P1 = \frac{43200}{1.08} = 40,000 \]

3. **Calculate the Present Value of the Second Payment (P2):**
- For the second payment (end of year 2):
- A2 = 34,992
- T2 = 2 years
- Substitute the values into the formula:
\[ P2 = \frac{34992}{(1 + \frac{8}{100})^2} = \frac{34992}{(1.08)^2} \]
- Calculate (1.08)^2:
\[ (1.08)^2 = 1.1664 \]
- Now substitute back to find P2:
\[ P2 = \frac{34992}{1.1664} \approx 30,000 \]

4. **Calculate the Total Sum Borrowed:**
- The total sum borrowed (S) is the sum of P1 and P2:
\[ S = P1 + P2 = 40,000 + 30,000 = 70,000 \]

### Final Answer:
The sum borrowed is Rs 70,000.

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