Question

A bill of Rs. 60,000 payable 10 months after date was discounted for Rs. 57,300 on 30th June 2007. If the rate of interest was $11\dfrac{1}{4}%$ per annum, on what date was the bill drawn?

Answer 1

Hint:Use the formula Banker’s discount BD = FV – A,where FV is Face value and A is amount received. Equate this to $BD=\dfrac{A\times R\times T}{100}$ to get the remaining period. Then use the formula Legal due date = Date of discount + Remaining period to find the Legal due date. Subtract the grace period of 3 days to find the nominal due date. Further subtract the given period of 10 months from this nominal due date to get the date of drawing which is the final answer.

Complete Complete step by step answer:
In this question, we are given that a bill of Rs. 60,000 payable 10 months after date was discounted for Rs. 57,300 on 30th June 2007. The rate of interest was $11\dfrac{1}{4}%$ per annum.
Using this information, we need to find the date on which the bill was drawn.
Here, we know that Banker’s Discount = Face Value – Amount received i.e BD = FV – A
So, BD = Rs. (60000-57300) = Rs. 2700
Now, BD is interested in face value for the remaining period.
Let the remaining period be n years.
Using this, we will have the following:
$2700=\dfrac{60000\times 11\dfrac{1}{4}\times n}{100}$
$2700=\dfrac{60000\times \dfrac{45}{4}\times n}{100}$
$n=\dfrac{2700\times 400}{60000\times 45}=0.4$ years
Now, we will convert this remaining period in years to days.
So, 0.4 years = $\dfrac{4}{10}\times 365=146$ days.
We will find the remaining number of days in each month from July 2007.
July : 31 days
August : 31 days
September : 30 days
October : 31 days
November : 23 days
Total : 146 days
Now we know that Legal due date = Date of discount + Remaining period.
Using this, we will get the following:
Legal due date = Date of discount + 146 days
Legal due date = 30 June 2007 + 146 days
Legal due date = 23 November 2007
So, using this Legal due date, we will find the nominal due date by subtracting a grace period of 3 days from the legal due date.
Nominal due date=20 November 2007.
Now, we will subtract 10 months from this nominal due date to get the date of drawing of bill.
Hence, the Date of Drawing of bill is 20 January 2007.
This is the final answer.

Note: In this question, it is very important to note that the duration of 10 months is subtracted from the nominal due date and not the legal due date. So, we need to find the nominal due date from the legal due date by subtracting a grace period of 3 days from the legal due date. It is a very common mistake to forget doing this step.