Question

A bill of $Rs.5050$ is drawn on ${13}^{th}April2013$. It was discounted on $4^{th}July2013$ at $5$% per annum. If the banker's gain on the transaction is $Rs.0.50$, 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 $A=Rs.5050$

Rate $i=5$% $p.a.=0.05$, Banker's gain $(B.G.)=Rs.0.50$

$B.G.=\frac{A(ni{)}^2}{1+ni}$

$0.50=\frac{5050(n\times 0.05{)}^2}{1+n\times 0.05}$

$5050n^2\times 0.0025=0.50+0.025n$

$12625n^2-25n-500=0$

$505n^2-n-20=0$

$505n^2-101n+100n-20=0$

$101n(5n-1)+20(5n-1)=0$

$(5n-1)(101n+20)=0$

$\Rightarrow n=\frac{1}{5}$ or $-\frac{20}{101}$ (not acceptable because of negative value)

$\therefore n=\frac{1}{5}years=\frac{365}{5}=73days$

$=\left[July\right(27days)+August(31days)+September(15day\left)\right]$

Hence, the legal due date is $15September$ and nominal due date is $12September$