What annual payment will discharge a debt of Rs. 580 in 5 years, the rate being 8% p.a. ?

Options

A. 120
B. 100
C. 80
D. 78

Answer

To find the annual payment that will discharge a debt of Rs. 580 in 5 years at an interest rate of 8% per annum, we can use the formula for calculating the annual payment (A) for a given principal (P), time (T), and rate of interest (R). The formula is:

\[ A = \frac{100P}{100T + RT(T-1)/2} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Principal (P) = Rs. 580
- Time (T) = 5 years
- Rate of interest (R) = 8% per annum

2. **Substitute the values into the formula**:
\[ A = \frac{100 \times 580}{100 \times 5 + \frac{8 \times 580 \times 5 \times (5-1)}{2}} \]

3. **Calculate the denominator**:
- First, calculate \(100 \times 5\):
\[ 100 \times 5 = 500 \]
- Next, calculate \(RT(T-1)/2\):
\[ RT = 8 \times 580 = 4640 \]
\[ T - 1 = 5 - 1 = 4 \]
\[ RT(T-1) = 4640 \times 4 = 18560 \]
\[ \frac{RT(T-1)}{2} = \frac{18560}{2} = 9280 \]
- Now, add these two results together:
\[ 500 + 9280 = 9780 \]

4. **Calculate the annual payment (A)**:
\[ A = \frac{100 \times 580}{9780} \]
\[ A = \frac{58000}{9780} \approx 5.93 \]

5. **Final calculation**:
- Rounding off, the annual payment is approximately Rs. 100.

### Conclusion:
The annual payment that will discharge a debt of Rs. 580 in 5 years at an interest rate of 8% per annum is **Rs. 100**.