A man wants to sell his scooter. There are two offers, one at ₹ 12,000 cash and the other at a credit of ₹ 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer?

### Concept & Present Worth Comparison To compare a cash offer today with a credit offer in the future, we must bring both to the same timeline. We do this by calculating the Present Worth (PW) of the future credit offer and comparing it directly to the cash offer. $$ \text{PW} = \frac{100 \times \text{Amount}}{100 + (R \times T)} $$ ### Step-by-Step Solution - First Offer (Cash): ₹ 12,000 today. - Second Offer (Credit): Amount (A) = ₹ 12,880 - Time (T) = 8 months = $\frac{8}{12}$ years = $\frac{2}{3}$ years - Rate (R) = 18% per annum - Calculate the Present Worth of the credit offer: $$ \text{PW} = \frac{100 \times 12880}{100 + (18 \times \frac{2}{3})} $$ $$ \text{PW} = \frac{1288000}{100 + 12} = \frac{1288000}{112} $$ - Solving the division: $1288000 / 112 = 11500$. - The Present Worth of the credit offer is ₹ 11,500. - Compare the two offers: ₹ 12,000 (cash) > ₹ 11,500 (present worth of credit). ### Exam Strategy & Shortcut Evaluate the effective interest percentage for 8 months at 18% p.a., which is $18\% \times (2/3) = 12\%$. This means the credit amount is 112% of its present worth. Divide 12,880 by 1.12. Recognising that $112 \times 100 = 11200$, you can estimate the value is slightly over 11,000, which is clearly less than 12,000. ### Common Pitfall Directly comparing the raw numbers (12,880 vs 12,000) and incorrectly assuming the higher absolute number is better without adjusting for the time value of money. ### Final Answer Therefore, the correct answer is **₹ 12,000 in cash**.