Bankers Discount - Quantitative Aptitude Video Lecture | Quantitative for GMAT

hey everyone in this video we are going
to talk about bankers discount so to
understand this topic let us consider a
scenario where two people deal with each
other so the two people are a and B and
a buy some goods from B these goods are
worth one thousand rupees and a does not
have immediate cash with him so what a
does is that a issues a bill of exchange
to B so this bill of exchange is
basically similar to a check and this
bill of exchange allows me to withdraw
money directly from the account of E but
this bill of exchange is usually at
credit so the bill of exchange is worth
rupees 1000 and at credit of five months
let's say so after five months we can go
to a bank and withdraw money worth 1000
piece from is account now the validity
of this bill of exchange is of five
months right so the date after exactly
five months is known as the nominally
due date and three days are given as
grace days and the date after three days
of the nominally due date is known as
the legally due date that is the last
date on which the bill of exchange can
be converted to the cash right now
consider that B is in urgent need of
money and he wants this money before the
legally due date let's say he wants this
money after three months instead of five
months so what we can do is that he can
go to a bank and give them this bill of
exchange and note that this is happening
after three months right so after
accepting this bill of exchange the bank
will give money to B but will it give a
total of 1000 rupees that means the
amount that was stated in the bill of
exchange no it will not give the total
amount why because obviously the bag
we'll make its profit right it will keep
some money so how much money will it
keep well the bank will deduct some
money which is known as the bankers
discount from the face value that is
from the value that was stated in the
bill of exchange right so the amount
deducted from the bill of exchange is
known as the bankers discount okay so
how does this Bank calculate the bankers
discount
well the bankers discount is nothing but
the simple interest on the face value
that is stated in the bill of exchange
for some certain rate decided by the
bank and for the period that is
remaining right so how much period is
remaining well about two months and
three days are remaining right so again
the bankers discount is the interest on
the face value of the bill of exchange
at some are percentage the rate defined
by the bank and for the time period
remaining right the remaining period
till the legally due date so if I have
to state the formula for calculating the
bankers discount it will be equals to
the amount that is stated in the bill of
exchange times n times the rate of
interest decided by the bank upon 100
basically the formula for calculating
the simple interest now there's another
term called as bankers gain which is the
actually the profit earned by the bank
while undertaking this transaction so it
is basically the bankers discount minus
the true discount so the profit obtained
by the bank can be calculated by
deducting the true discount for the
expired time and then deducting it from
the bankers discount right so we know
these two formulas let us solve a
problem now so the question is a bill
for 6000 rupees is drawn on July 14th at
five months it is discounted on fifth
October at 10% find the bankers discount
true discount bankers gain and the money
that the holder of the bill receives
okay so we have been given the face
value of this bill that is the amount it
is six thousand rupees now we will have
to calculate the nominally due date and
the legally due date right so for that
we have been given on what date
this bill is drawn so the spill is drawn
on July 14th and the validity is five
months right so the nominally due date
will be five months after the date on
which this bill was drawn okay
so July 14th plus five months is
actually December 14th right so the
nominally due date will be December 14th
now we need to calculate the legally due
date and the legally due date is
actually three days after the nominal
due date right so it is December 17th
now what is the formula for bankers
discount well bankers discount is equals
to the simple interest on the amount
right and what will be the rate here the
rate has been fixed at 10% so at 10
percent for the unexpired time now how
do you calculate this uh nex-5 time so
the unexpired time will be the time from
you know the date at which the bill was
discounted till the legally due date
right so we will have to calculate how
many number of years does the time from
5th October till December 17th
constitute right so the unexpired time
will be the number of days in October
plus the number of days in November plus
the number of days in December right so
the bill was discounted on 5th October
so how many number of days are remaining
till 31st October because October is up
31 days so 31 minus 5 that's 26 so we
have 26 days in October plus November is
of 30 days so plus 30 plus the
Corelli due date is December 17th so we
will take the 17 first days of December
right so 26 plus 30 plus 17 is 73 days
right now you need to convert this into
years
okay so 73 by 365 years and that is
actually 1 by 5 years so we've got the
time period now we can calculate the
bankers discount right so this is the
simple interest on the amount so what is
the amount amount is 6000 so 6000 times
n n is 1 by 5 years so 1 by 5 times the
rate is 10 upon hundred okay 5 times 2
is 10 and these zeros get cancelled out
so 60 times 2 that's 120 rupees is the
bankers discount now you need to
calculate true discount this true
discount will be calculated on the
amount of 6000 rupees right so you know
the formula for true discount that is
amount times n times R upon 100 plus n
times R right so this is equals to 6000
times 1 by 5 times 10 upon I have 100
plus 1 by 5 times 10 right so 5 times 2
is 10 and 5 times 2 is 10 here also and
if you calculate this you will get the
value as 117 0.64 right so this is the
true discount now what is remaining we
have to calculate what is the bankers
gain so bankers gain is actually the
bankers discount minus the true discount
isn't it we just saw that so 120 minus
one hundred and seventeen point six four
and that is equal to two point three six
rupees right so that is the bankers gain
that means the profit that the bank
makes now lastly we need to calculate
how much money is given to the holder of
the bill
right how much money is returned well
the money received by the holder of the
bill will be the amount that was stated
in the bill of exchange - the bankers
discount the bank keeps the bankers
discount with itself and gives the rest
of the money to the holder of the bill
right so money returned will be equal to
the amount is 6000 - the bankers
discount is 120 rupees so this is equals
to five thousand eight hundred and
eighty rupees the money returned so this
is how you solve problems on bankers
discount