Jagatram, a trader, owes a merchant Maganlal Rs 5014 due 1 yr hence. Jagatram wants to settle the ac-count after 3 months. If the rate of interest is 12% per annum, how much cash should Jagatram pay?

Options

A. Rs 9200
B. Rs 5600
C. Rs 4600
D. Rs 6600

Answer

To solve the problem, we need to find out how much cash Jagatram should pay today to settle a debt of Rs 5014 that is due in 1 year, given that he wants to settle it after 3 months. The interest rate is 12% per annum.

### Step-by-Step Solution:

1. **Identify the Time Periods**:
- The total time until the debt is due is 1 year (12 months).
- Jagatram wants to pay after 3 months, so the remaining time until the debt is due is:
\[ 12 \text{ months} - 3 \text{ months} = 9 \text{ months} \]

2. **Determine the Present Worth**:
- We need to calculate the present worth (PW) of the amount due (Rs 5014) after 9 months.
- The formula for present worth is:
\[ PW = \frac{F}{(1 + r)^n} \]
- Where:
- \( F \) = Future value (the amount due) = Rs 5014
- \( r \) = Rate of interest per period (in decimal) = \(\frac{12}{100} = 0.12\)
- \( n \) = Number of periods (in years) = \(\frac{9}{12} = 0.75\) years

3. **Calculate the Present Worth**:
- First, calculate the total interest factor for 9 months:
\[ (1 + r)^{n} = (1 + 0.12)^{0.75} \]
- To simplify, we can also use the formula:
\[ PW = \frac{5014}{1 + \frac{12 \times 9}{100 \times 12}} = \frac{5014}{1 + 0.09} = \frac{5014}{1.09} \]

4. **Perform the Calculation**:
- Calculate the denominator:
\[ 1 + 0.09 = 1.09 \]
- Now calculate the present worth:
\[ PW = \frac{5014}{1.09} \approx 4600 \]

5. **Conclusion**:
- Jagatram should pay approximately Rs 4600 in cash to settle the account after 3 months.

### Final Answer:
Jagatram should pay Rs 4600.