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प्रश्न
A bill drawn on 5th June for 6 months was discounted at the rate of 5% p.a. on 19th October. If the cash value of the bill is ₹ 43,500, find face value of the bill.
उत्तर
Given, Date of drawing = 5th June
Period of the bill = 6 months
∴ Nominal due date = 5th December
Legal due date = 8th December
Date of discounting = 19th October
Cash value (C.V.) = ₹ 43,500 and r = 5%
Now, number of days from the date of discounting to the legal due date are as follows:
| Oct | Nov | Dec | Total |
| 12 | 30 | 8 | 50 |
∴ n = `50/365 = 10/73` years
Let F.V. of the bill be x.
C.V. = F.V. – B.D.
`43,500 = x - ("F.V" xx "n" xx "r")/100`
`43,500 = x - ("x" xx 10/73 xx 5)/100`
`43,500 = x - ("x" xx 10 xx 5)/(73 xx 100)`
`43,500 = x(1 - 1/146)`
`43,500 = x xx 145/146`
x = `43,500 xx 146/145`
x = ₹ 43,800
∴ Face value of the bill is ₹ 43,800.
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Choose the correct alternative:
The date on which the period of the bill expires is called ______
A bill of ₹ 8,000 drawn on 5th January 2019 for 8 months was discounted for ₹ 7,680 on a certain date. Find the date on which it was discounted at 10% p.a.
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
| April | May | June | July | Aug | Sep | Total |
| 15 | 31 | 30 | 31 | 31 | `square` | `square` |
∴ Date of discounting is `square`
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The banker’s discount is also called true discount.
