Question

A bill drawn on 5^th June for 6 months was discounted at the rate of 5% p.a. on 19^th October. If the cash value of the bill is ₹ 43,500, find face value of the bill.

Answer 1

Given, Date of drawing = 5^th June

Period of the bill = 6 months

∴ Nominal due date = 5^th December

Legal due date = 8^th December

Date of discounting = 19^th October

Cash value (C.V.) = ₹ 43,500 and r = 5%

Now, number of days from the date of discounting to the legal due date are as follows:

Oct	Nov	Dec	Total
12	30	8	50

∴ n = `50/365 = 10/73` years

Let F.V. of the bill be x.

C.V. = F.V. – B.D.

`43,500 = x - ("F.V" xx "n" xx "r")/100`

`43,500 = x - ("x" xx 10/73 xx 5)/100`

`43,500 = x - ("x" xx 10 xx 5)/(73 xx 100)`

`43,500 = x(1 - 1/146)`

`43,500 = x xx 145/146`

x = `43,500 xx 146/145`

x = ₹ 43,800

∴ Face value of the bill is ₹ 43,800.