Question

A bill of a certain sum drawn on 28^th February 2007 for 8 months was encashed on 26^th March 2007 for ₹ 10,992 at 14% p.a. Find the face value of the bill.

Answer 1

We know that, Banker’s discount (B.D.) = Face value – Cash value

∴ B.D. = F.V. – 10,992   .....(i)

Date of bill drawn = 28^th February 2007

Date of bill discounting = 26^th March 2007

Period of bill = 8 months

∴ Nominal due date = 28^th October 2007

∴ Legal due date = 31^st October 2007

∴ Number of days from date of bill discounting to legal due date:

March	April	May	June	July	August	September	October	Total
5	30	31	30	31	31	30	31	219

∴ 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.