Sunil borrowed some money on compound in terest and returned it in three years in equal annual instalments. If the rate of interest is 15% per annum and annual instalments are ₹365010 each find the sum borrowed :

Options

A. 1112220
B. 1111200
C. 834400
D. 833400

Answer

To solve the problem of finding the sum borrowed by Sunil, we can use the formula for the present value of an annuity since he is paying back the loan in equal annual installments.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Annual installment (A) = ₹365010
- Rate of interest (r) = 15% per annum = 0.15
- Number of years (n) = 3

2. **Formula for Present Value of Annuity**:
The present value (PV) of an annuity can be calculated using the formula:
\[ PV = A \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \]

3. **Substituting the Values**:
Substitute the values into the formula:
\[ PV = 365010 \times \left( \frac{1 - (1 + 0.15)^{-3}}{0.15} \right) \]

4. **Calculating (1 + r)^{-n}**:
First, calculate \( (1 + 0.15)^{-3} \):
\[ (1 + 0.15) = 1.15 \]
Then,
\[ (1.15)^{-3} \approx 0.6575 \quad (\text{using a calculator}) \]

5. **Calculating the Present Value**:
Now substitute back into the formula:
\[ PV = 365010 \times \left( \frac{1 - 0.6575}{0.15} \right) \]
\[ PV = 365010 \times \left( \frac{0.3425}{0.15} \right) \]
\[ PV = 365010 \times 2.2833 \quad (\text{approximately}) \]
\[ PV \approx 834,999.83 \]

6. **Final Result**:
The sum borrowed by Sunil is approximately ₹835000.