Question

A bill was drawn on 14^th April 2005 for ₹ 3,500 and was discounted on 6^th July 2005 at 5% per annum. The banker paid ₹ 3,465 for the bill. Find the period of the bill. 

Answer 1

Given, Face value = ₹ 3,500,

Date of drawing = 14^th April 2005,

Date of discount = 6^th July 2005,

r = 5% p.a.

Cash value = ₹ 3,465

Since, B.D. = F.V. – C.V.

∴ B.D. = 3,500 – 3,465

∴ B.D. = ₹ 35

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

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

i.e., `35 = (3,500 xx n xx 5)/100`

i.e., 35 = 35 × n × 5

i.e., 5n = 1

i.e., n = `1/5` year = `1/5 xx 365 = 73` days

∴ Period for which the discount is deducted is 73 days, which is counted from date of discounting i.e., 6th July 2005

July	Aug	Sept	Total
25	31	17	73

∴ Legal due date is 17^th September 2005

∴ Nominal due date is 14^th September 2005

∴ Period of the bill is from 14^th April 2005 to 14^th September 2005 i.e., 5 months

∴ Period of the bill is 5 months.