Question

A bill of ₹ 5050 is drawn on 13th April 2013. It was discounted on 4th July 2013 at 5% per annum. If the banker’s gain on the transaction is ₹ 0.50, find the nominal date of the maturity of the bill.

Answer 1

Let the unexpired time period of the bill at the time of discount be n years.
Face value A = ₹ 5050
Rate i = 5% p.a. = 0.05, Banker's gain (B.G.) = ₹ 0.50

B.G. = `("A"(ni)^2)/(1 + ni)`

0.50 = `(5050 (n xx 0.05)^2)/(1 + n  xx 0.05)`

5050n² x 0.0025 = 0.50 + 0.025n
12625n² - 25n - 500 = 0
505n² - n - 20 = 0
505n² - 101n + 100n - 20 = 0
101n ( 5n - 1) + 20 (5n - 1) = 0
(5n - 1) (101n + 20) = 0

⇒ `n = (1)/(5) or -(20)/(101)` Rejecting-Ve value, ∵ time cannot -Ve

∴ `n = (1)/(5)` years = 73 days

= [ July (27 days) + August (31 days) + September (15 days) ]

Hence, the nominal due date is 15 September.