Question

A bill of ₹ 65,700 drawn on July 10 for 6 months was discounted for ₹ 65,160 at 5% p.a. on what day was the bill discounted?

Answer 1

Given, Face value = ₹ 65,700

Date of drawing = 10^th July

Period of the bill = 6 months

∴ Nominal due date = 10^th January

Legal due date = 13^th January

r = 5% p.a.

Cash value = ₹ 65,160

Since, B.D. = F.V. – C.V. = 65,700 – 65,160

∴ B.D. = ₹ 540

But, B.D. = interest on F.V. for n years at r %

i.e., B.D. = `("F.V." xx "n"/365 xx "r")/100`

∴ 540 =  `(65,700 xx "n" xx 5)/(100 xx 365)`

∴ n = `(540 xx 365 xx 100)/(65700 xx 5)`

∴ n = 60 days

∴ Discount is deducted for 60 days.

Thus, the bill is discounted 60 days before 13^th January.

Jan	Dec	Nov	Total
13	31	16	60

∴ Date of discounting the bill is 14^th November.