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.

#### Solution

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

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