Discussion
A bill falls due in 1 year.The creditor agrees to accept immediate payment of the half and to defer the payment of the other half for 2 years.By this arrangement ins Rs.40.what is the amount of the bill,if he money be worth 12.5%?
Answer: C
Let the bill be \( A \), due in 1 year, with money worth \( 12.5\% \).
Original arrangement - the whole bill in 1 year:
\[ \text{PW}_{\text{old}} = \frac{A}{1 + 0.125} = \frac{A}{1.125} = 0.8889\,A \]
New arrangement - half now (no discount) and half in 2 years:
\[ \text{PW}_{\text{new}} = \frac{A}{2} + \frac{A/2}{1 + 0.25} = 0.5A + 0.4A = 0.9A \]
The creditor gains the difference:
\[ 0.9A - 0.8889A = 0.01111\,A = 40 \]
\[ A = \frac{40}{0.01111} = \text{Rs. } 3600 \]
Deferring half by a further year costs less than being paid the other half a year early gains - because discounting bites harder on the nearer payment.
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