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Question
A bill of ₹ 65,700 drawn on July 10 for 6 months was discounted for ₹ 65,160 at 5% p.a. On what day was the bill discounted?
Solution
Given, Face value = ₹ 65,700
Date of drawing = 10th July
Period of the bill = 6 months
∴ Nominal due date = 10th January
Legal due date = 13th January
r = 5% p.a.
Cash value = ₹ 65,160
Since, B.D. = F.V. – C.V. = 65,700 – 65,160
∴ B.D. = ₹ 540
But, B.D. = interest on F.V. for n years at r %
i.e., B.D. = `("F.V." xx "n"/365 xx "r")/100`
∴ `540 = (65700 xx "n" xx 5)/(100 x 365)`
∴ n = `(540 xx 365 xx 100)/(65700 xx 5)`
∴ Discount is deducted for 60 days. Thus, the bill is discounted 60 days before 13th January.
| Jan | Dec | Nov | Total |
| 13 | 31 | 16 | 60 |
∴ Date of discounting the bill is 14th November.
Notes
The answer in the textbook is incorrect.
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Solution: Banker’s Discount
B.D.= F.V. − C.V. = 8,000 −7,680 = ₹ 320
Date of drawing = 5th January 2019
Period = 8 months
Nominal due date = `square`
Legal due date = `square`
B.D. = Interest on F.V. for n at 10% p.a.
∴ B.D. = `("F.V." xx "n"/365 xx "r")/100`
∴ 320 = `(8000 xx "n"/365 xx 10)/100`
∴ n = `square` days
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| 15 | 31 | 30 | 31 | 31 | `square` | `square` |
∴ Date of discounting is `square`
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