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Question
A bill was drawn on 14th April 2005 for ₹ 3,500 and was discounted on 6th July 2005 at 5% per annum. The banker paid ₹ 3,465 for the bill. Find the period of the bill.
Solution
Given, Face value = ₹ 3,500,
Date of drawing = 14th April 2005,
Date of discount = 6th July 2005,
r = 5% p.a.
Cash value = ₹ 3,465
Since, B.D. = F.V. – C.V.
∴ B.D. = 3,500 – 3,465
∴ B.D. = ₹ 35
But, B.D. = interest on F.V. for n years at r % p.a.
i.e. B.D. = `(F.V. xx n xx r)/100`
i.e., `35 = (3,500 xx n xx 5)/100`
i.e., 35 = 35 × n × 5
i.e., 5n = 1
i.e., n = `1/5` year = `1/5 xx 365 = 73` days
∴ Period for which the discount is deducted is 73 days, which is counted from date of discounting i.e., 6th July 2005
| July | Aug | Sept | Total |
| 25 | 31 | 17 | 73 |
∴ Legal due date is 17th September 2005
∴ Nominal due date is 14th September 2005
∴ Period of the bill is from 14th April 2005 to 14th September 2005 i.e., 5 months
∴ Period of the bill is 5 months.
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