I want to sell my scooter. There are two offers. One at cash payment of Rs. 8100 and another at a credit of Rs. 8250 to be paid after 6 months. If money being worth `6 ¼%` per annum simple interest, which is the better offer?

Options

A. Rs. 8100 in cash
B. Rs. 8250 due 6 months hence
C. Both are equally good
D. Can’t be said

Answer

To determine which offer is better for selling the scooter, we need to compare the present value of the credit offer with the cash offer. Here’s how we can do it step by step:

### Step-by-Step Solution:

1. **Identify the Offers**:
- Cash offer: Rs. 8100
- Credit offer: Rs. 8250 (to be paid after 6 months)

2. **Determine the Rate of Interest**:
- The interest rate is given as 6 ¼% per annum.
- Convert this to a fraction:
\[ 6 \frac{1}{4}\% = \frac{25}{4}\% = 0.0625 \]

3. **Calculate the Present Value of the Credit Offer**:
- The formula for calculating the present value (PV) using simple interest is:
\[ PV = \frac{Future\ Value}{(1 + r \cdot t)} \]
- Here, \(Future\ Value = 8250\), \(r = 0.0625\), and \(t = \frac{6}{12} = 0.5\) years.
- Substitute the values into the formula:
\[ PV = \frac{8250}{(1 + 0.0625 \cdot 0.5)} \]

4. **Calculate the Denominator**:
- First, calculate \(0.0625 \cdot 0.5 = 0.03125\).
- Therefore, \(1 + 0.03125 = 1.03125\).

5. **Calculate the Present Value**:
- Now substitute back into the equation:
\[ PV = \frac{8250}{1.03125} \approx 8000 \]

6. **Compare the Present Value with Cash Offer**:
- Cash offer: Rs. 8100
- Present value of credit offer: Rs. 8000
- Since Rs. 8100 > Rs. 8000, the cash offer is better.

### Conclusion:
The cash payment of Rs. 8100 is the better offer compared to the credit payment of Rs. 8250 after 6 months.

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