A bill of ₹ 5,475 drawn on 19th January 2015 for 8 months was discounted on 28th February 2015 at 8% p.a. interest. What is the banker's discount? What is the cash value of the bill?

Answer: Banker's discount = ₹ 247.20; cash value = ₹ 5,227.80

Date of drawing: 19 January 2015; period 8 months. Nominal due date: 19 September 2015. Legal due date (adding 3 days of grace): 22 September 2015.

Number of days from 28 February 2015 to 22 September 2015:
Feb 0 + Mar 31 + Apr 30 + May 31 + Jun 30 + Jul 31 + Aug 31 + Sep 22 = 206 days \(=\frac{206}{365}\) year.

Banker's discount \(=\text{F.V.}\times n\times\frac{r}{100}=5475\times\frac{206}{365}\times\frac{8}{100}=15\times 206\times 0.08=₹\,247.20\)

Cash value \(=5475-247.20=₹\,5227.80\)