Discussion
A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 12% per annum, how much cash should he pay?
Answer: B
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:
\[ \text{Amount} = \text{PW}\left(1 + \frac{RT}{100}\right), \qquad \text{TD} = \text{Amount} - \text{PW} \]
The debt falls due in 1 year and is being settled after 3 months, so it is being paid 9 months early. Only that unexpired period is discounted.
\[ T = \frac{9}{12} = \frac{3}{4} \text{ year}, \qquad \frac{RT}{100} = \frac{12 \times 3/4}{100} = 0.09 \]
\[ \text{PW} = \frac{10028}{1.09} = 9200 \]
So he should pay Rs. 9200. The commonest error is discounting for the full year rather than for the nine months actually saved.
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