Question

A bill for rupees 7,650 was drawn on 8th March,2013, at 7 months. It was discounted on 18th May,2013 and the holder of the bill received rupees 7,497. What is the rate of interest charged by the bank?

Answer 1

Hint: Use relation banker’s discount = Bill amount $\times $unexpired period $\times $interest /100
Calculate unexpired period by using difference in legally due date and discounted date.

Complete Step-by-step answer:
Here, it is given that Bill was drawn on the 8th March 2013 for 7 months.
Hence date after 7 months from 8th March be 8th October 2013.
And as we know, 8th October 2013 is termed as normal due date as per the terminology.
Hence, normal due date = 8th October, 2013
And as we know the relation as
Legally due date = Normal due date + 3
Hence, legal due date = 11th October, 2013
As, bill was discounted on 18th May 2013
$\because $The unexpired period of the bill can be calculated as
         May - 13 days
     June - 30 days
     July - 31 days
     August - 31 days
     September - 30 days
     October - 11 days
Now, adding the above number of the days, we get
unexpired period of the bills = 13 + 30 + 31 + 31 + 30 + 11
                        = 146 days
We can represent days to year by dividing 146 days by 365. Hence, we get
     unexpired period\[=\dfrac{146}{365}=\dfrac{2}{5}\] yrs
As we know that
Banker’s discount = Total amount of bill drawn – Total amount received by holder
Hence, we can put values in the above equation to get a banker's discount as the amount of bill drawn was 7650 and bill received 7497. Hence, we get
banker’s discount = 7650 – 7497
              = 153 Rs
Now, we can use identity of banker’s discount in terms of unexpired period and interest by the bank and amount of bill as banker’s discount = Bill amount $\times $ unexpired period $\times $ interest rate /100
\[153=\dfrac{7650\times 2\times i}{100\times 5}\]
where i = interest rate
On simplifying above equation, we get
On cross multiplying the above equation, we get
\[\dfrac{153\times 5\times 100}{7650\times 2}=i\]
\[\dfrac{153\times 25}{765}=i\]
or \[i=\dfrac{153\times 5}{153}=5%\]
Hence, the required rate of interest is 5% per annum.

Note: One can put the amount received by the holder in place of the bill amount while using the formula of the Banker's discount. It is a general confusion by students. Hence, be clear with all the terminologies in Banker’s discount topic.
Bill amount is also termed as the face value of the debt. Unexpired time is the difference between legally due date and the date on which the bill was discounted. One can go wrong with the unexpired time as well. One can take unexpired time as the difference between legally due date and date on which bill was drawn which is wrong. Hence, be careful with the terminology while solving these kind of problems.