Cash vs. credit offer comparison with time value: A scooter has two offers: (i) Rs. 8100 cash today, (ii) Rs. 8250 to be paid after 6 months. Money is worth 6 1/4% per annum (simple interest). Which offer is better?

Introduction / Context:
When comparing a cash price to a deferred-payment price, we convert the deferred amount to its present worth using the stated simple-interest rate. The higher present worth is preferable for the seller; for the buyer choosing between offers, the lower present worth outflow is the better deal to accept as “value received.”

Given Data / Assumptions:

• Offer 1: 8100 now.
• Offer 2: 8250 after 6 months (0.5 years).
• Rate = 6 1/4% = 6.25% per annum simple interest.

Concept / Approach:
Present worth PW of the delayed amount: PW = A / (1 + r * t). Compare PW of 8250 with 8100 paid today. The better offer for the recipient (seller) is the one with larger PW; for a buyer selecting the payment mode, the better offer is the one that costs less in present terms. Here we simply see which figure is larger/smaller.

Step-by-Step Solution:
t = 0.5 years; r = 6.25% = 0.0625.PW (credit) = 8250 / (1 + 0.0625 * 0.5) = 8250 / 1.03125.Since 1.03125 = 33/32, PW = 8250 * 32 / 33 = 8000.Compare: cash = 8100 vs PW(credit) = 8000. For a seller, cash is better; for the buyer assessing which is “more valuable,” the cash outflow 8100 is larger than 8000 PW of credit, so choosing cash offer (as a sale price) is more costly. The question asks “which is the better offer?” Conventionally, the better quotation for the seller to accept is the higher PW — that is 8100 cash.

Verification / Alternative check:
If money is worth 6.25% p.a., taking 8250 after 6 months effectively equals 8000 now. Since 8100 now > 8000 now, 8100 cash is better for the recipient.

Why Other Options Are Wrong:

• “8250 due 6 months hence” is inferior (PW = 8000).
• “Both are equally good” is incorrect (8100 ≠ 8000).
• “Can’t be said” is unnecessary; the rate is given.

Common Pitfalls:

• Using compound interest accidentally; the problem is explicitly simple interest.
• Forgetting to convert 6 months to 0.5 years.

Final Answer:
Rs. 8100 in cash