Discussion
A man wants to sell his scooter. There are two offers, one at Rs. 12,000 cash and the other a credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer?
Answer: A
The present worth (PW) is what the sum is really worth today; the true discount (TD) is the interest that PW would earn over the remaining time:
\[ \text{Amount} = \text{PW}\left(1 + \frac{RT}{100}\right), \qquad \text{TD} = \text{Amount} - \text{PW} \]
Bring the credit offer back to today's money and then compare like with like.
\[ T = \frac{8}{12} = \frac{2}{3} \text{ year}, \qquad \frac{RT}{100} = \frac{18 \times 2/3}{100} = 0.12 \]
\[ \text{PW of the credit offer} = \frac{12880}{1.12} = 11500 \]
\[ 12000 > 11500 \]
The cash offer is worth Rs. 500 more in today's money, so Rs. 12,000 in cash is the better deal. The larger headline figure loses because eight months at 18% costs more than the extra Rs. 880 is worth.
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