The annual payment will discharge a debt of Rs. 5082 due in 2 yr at `10%` per annum compounded annually is

Options

A. Rs. 1420
B. Rs. 1440
C. Rs. 1419
D. Rs. 2420

Answer

To find the annual payment that will discharge a debt of Rs. 5082 due in 2 years at an interest rate of 10% per annum compounded annually, we can use the formula for calculating the annual payment for a compound interest loan.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Principal (P) = Rs. 5082
- Rate of interest (r) = 10% per annum
- Time (t) = 2 years

2. **Use the Formula for Annual Payment**:
The formula for the annual payment (A) that will discharge a debt is given by:
\[ A = \frac{P \cdot r(1 + r)^t}{(1 + r)^t - 1} \]
where \( r \) is expressed as a decimal.

3. **Convert the Rate to Decimal**:
Since the rate is given in percentage, we convert it to decimal:
\[ r = \frac{10}{100} = 0.10 \]

4. **Substitute the Values into the Formula**:
Now substitute the values into the formula:
\[ A = \frac{5082 \cdot 0.10(1 + 0.10)^2}{(1 + 0.10)^2 - 1} \]

5. **Calculate \((1 + r)^t\)**:
Calculate \((1 + 0.10)^2\):
\[ (1 + 0.10)^2 = 1.10^2 = 1.21 \]

6. **Calculate the Numerator**:
Now calculate the numerator:
\[ \text{Numerator} = 5082 \cdot 0.10 \cdot 1.21 = 508.2 \cdot 1.21 = 615.902 \]

7. **Calculate the Denominator**:
Calculate the denominator:
\[ \text{Denominator} = 1.21 - 1 = 0.21 \]

8. **Calculate the Annual Payment**:
Now, divide the numerator by the denominator:
\[ A = \frac{615.902}{0.21} \approx 2932.43 \]

9. **Round to the Nearest Rupee**:
The annual payment rounded to the nearest rupee is:
\[ A \approx Rs. 2932 \]

### Final Answer:
The annual payment that will discharge the debt of Rs. 5082 due in 2 years at 10% per annum compounded annually is approximately **Rs. 2932**.