A bill was drawn on 14th April for ₹ 7,000 and was discounted on 6th July at 5% p.a. The banker paid ₹ 6,930 for the bills. Find the period of the bill.

Answer: The period of the bill is 5 months.

Face value \(= ₹\,7000\), cash value \(= ₹\,6930\), so banker's discount B.D. \(= 7000 - 6930 = ₹\,70\).

B.D. \(= \dfrac{F \times n \times r}{100}\), where \(n\) is the unexpired period in years:

\(70 = \dfrac{7000 \times n \times 5}{100} = 350n \Rightarrow n = \dfrac{1}{5}\) year \(= \dfrac{365}{5} = 73\) days.

Counting 73 days from 6^th July: July 25 days (7 to 31), August 31 days (total 56), September 17 days (total 73). So the legal due date is 17^th September.

Nominal due date \(=\) legal due date \(-\) 3 days of grace \(=\) 14^th September.

From 14^th April (date of drawing) to 14^th September is 5 months. Hence the bill was drawn for 5 months.