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Question
The true discount on a sum is `3/8` of the sum due at 12% p.a. Find the period of the bill.
Solution
Given, T.D. =`3/8 xx`S.D.
∴ T.D. = `3/8 xx ("P.W." + "T.D.")`
∴ `8/3` T.D. = P.W. + T.D.
∴ P.W. = `8/3` T.D. - T.D.
∴ P.W. = `5/3` T.D.
Also, T.D. = `("P.W." xx "n" xx "r")/100`
∴ T.D. =`(5/3 "T.D." xx"n" xx 12)/100`
∴ T.D. = `(5 "T.D." xx "n" xx 12)/(3 xx 100)`
∴ n = `("T.D." xx 3 xx 100)/(5 "T.D." xx 12)`
∴ n = 5 years
∴ Period of the bill is 5 years.
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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
| April | May | June | July | Aug | Sep | Total |
| 15 | 31 | 30 | 31 | 31 | `square` | `square` |
∴ Date of discounting is `square`
The banker’s discount is also called true discount.
