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Question
A bill is drawn for ₹ 7,000 on 3rd May for 3 months and is discounted on 25th May at 5.5%. Find the present worth.
Solution
Sum due (S.D.) = ₹ 7,000
Period = 3 months
Date of bill drawn = 3rd May
Nominal due date = 3rd August
Legal due date = 6th August
Date of bill discounting = 25th May
Number of days from bill discounting date to legal due date
| May | June | July | August | Total |
| 6 | 30 | 31 | 6 | 73 days |
∴ True discount (T.D.) = `("P.W." xx "n" xx "r")/100`
`= ("P.W." xx 73/365 xx 5.5)/100`
∴ T.D. = `(1.1 "P.W.")/100` ...(i)
Also, S.D. = P.W. + T.D.
∴ `7,000 = "P.W." + (1.1 "P.W.")/100` ...[From (i)]
∴ `7,000 = (100 "P.W" + 1.1 "P.W.")/100`
∴ 7,000 × 100 = 101.1 P.W.
∴ P.W. = `(7,00,000)/101.1`
∴ P.W. = 6923.83 ≅ ₹ 6,923
∴ Present worth of bill drawn for ₹ 7,000 is ₹ 6,923.
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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`
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| April | May | June | July | Aug | Sep | Total |
| 15 | 31 | 30 | 31 | 31 | `square` | `square` |
∴ Date of discounting is `square`
