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Question
A bill of a certain sum drawn on 28th February 2007 for 8 months was encashed on 26th March 2007 for ₹ 10,992 at 14% p.a. Find the face value of the bill.
Solution
We know that,
Banker’s discount (B.D.) = face value – cash value
∴ B.D. = F.V. – 10,992 …(i)
Date of bill drawn = 28th February 2007
Date of bill discounting = 26th March 2007
Period of bill = 8 months
Nominal due date = 28th October 2007
Legal due date = 31st October 2007
Number of days from date of bill discounting to legal due date
| Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Total |
| 5 | 30 | 31 | 30 | 31 | 31 | 30 | 31 | 219 days |
∴ n = `219/365 = 3/5`
Since,
Banker’s discount = `("F.V." xx "n" xx "r")/100`
∴ F.V. – 10,992 = `("F.V." xx 3/5 xx 14)/100` ....…[From (i)]
∴ F.V. – 10,992 = `("F.V." xx 3 xx 14)/(100 xx 5)`
∴ F.V. – `(42 "F.V.")/500` = 10,992
∴ `(500 "F.V." - 42 "F.V.")/500 = 10,992`
∴ `(458 "F.V.")/500 = 10,992`
∴ F.V. = `10992 xx 500/458`
∴ F.V. = 12000
∴ Face value of the bill is ₹ 12,000
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