Question

A bill of ₹ 51,000 was drawn on 18^th February 2010 for 9 months. It was encashed on 28^th June 2010 at 5% p.a. Calculate the banker’s gain and true discount. 

Answer 1

It is given that,

Face value (F.V.) = ₹ 51,000 which is (S.D.)

Date of drawing = 18^th February 2010

Date of discounting = 28^th June 2010

Period of bill = 9 months

Nominal due date = 18^th November 2010

Legal due date = 21^st November 2010

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

June	July	Aug	Sep	Oct	Nov	Total
2	31	31	30	31	21	146 days

Rate = 5% p.a.

We know that,

T.D. = `("P.W." xx "n" xx "r")/100`

`= ("P.W." xx 146/365 xx 5)/100`

∴ T.D. = 0.02 P.W.        ...(i)

Since, S.D. = P.W. + T.D.

∴ S.D. = P.W. + 0.02 P.W.       …[From (i)]

∴ 51,000 = 1.02 P.W.

∴ P.W. = `(51,000)/1.02`

∴ P.W. = 50,000

Since T.D. = 0.02 × P.W.

= 0.02 × 50000

= ₹ 1000

∴ True discount is ₹ 1,000

Banker’s gain = `("T.D." xx "n" xx "r")/100`

`= (1000 xx 146/365 xx 5)/100`

= ₹ 20

∴ True discount is ₹ 1,000 and Banker’s gain is ₹ 20.