Question

A bill of Rs. 1,000 drawn on 7th May 2011 for six months was discounted on 29th August 2011 for cash payment of Rs. 988. Find the rate of interest charged by the bank.

Answer 1

Hint:Find the legally due date by adding the tenure (6 months) plus the grace period (3 days) to the date of drawing the bill. Find the unexpired number of days by subtracting the date of discounting of the bill from the legally due date. Next, use Banker's discount, B.D. = Face value - Amount realised and equate this to $BD=\dfrac{A\times n\times r}{100}$. Substitute all the values and solve for r which is the final answer.
Complete step-by-step answer:
In this question, we are given that a bill of Rs. 1,000 drawn on 7th May 2011 for six months was discounted on 29th August 2011 for cash payment of Rs. 988.
Using this information, we need to find the rate of interest charged by the bank.
The bill was drawn on : 07 . 05 . 2011
The given tenure is 6 Months.
So the nominal due date will be 6 months after the date the bill was drawn.
So, the nominal due date is : 07 . 11 . 2011
Now, we know that a 3 day grace period is given after the nominal due date. The date after this 3 day grace period is called the legally due date.
So, the legally due date is : 10 . 11 . 2011
The bill was discounted on 29 . 08 . 2011
We will now calculate the unexpired number of days which is the number of days left to the legally due date from the current date.
We will find the unexpired number of days in each month from August:
August : 2 days
September : 30 days
October : 31 days
November : 10 days
So, total number of unexpired days = 2 + 30 + 31 + 10 = 73 days
We will now divide this by 365 to find the time period as a fraction of a year.
So, time period, $n=\dfrac{73}{365}=\dfrac{1}{5}$ years
Now, we will calculate the bankers discount, BD. It is the simple interest on the face value (Rs. 1000) of the debt for the time period from the date on which the bill is discontinued to the legally due date.
i.e. $BD=\dfrac{A\times n\times r}{100}$
Now, Banker's discount, B.D. = Face value - Amount realised = Rs. 1000 - Rs. 988 = Rs. 12
Using this value and the above formula, we will get the following:
$12=\dfrac{1000\times \dfrac{1}{5}\times r}{100}$
$r=\dfrac{12\times 5\times 100}{1000}=6$
Hence, the required rate of Interest charged by the bank is 6% per annum.
This is our final answer.

Note: In this question, it is very important to note that when we calculate the time period or the unexpired number of days, it is important to divide this by 365 to convert this into a number of years as time period is taken in years. If we do not do this, we will get inappropriate answers.Students should remember the formula of Banker's discount and terms associated with it.