Bankers Discount
Formulae:
i. Suppose a merchant A buys goods worth Rs.10000 from another
merchant B at a credit of say 5 months
ii.Then,B prepares a bill , called the bill of exchange
iii. A signs this bill & allows B to withdraw the amount from his
bank account after exactly 5 months,the date exactly after
5 months is called Nominally due date
iv. Three days (grace days) are added to it get a date known as
legally due date
v.Suppose B wants to have money before legally due date then he
can have the money from banker or a broker who deducts S.I on the
face value (i.e., 10000) for the period from the date on which
the bill was discounted (i.e paied by the banker) & the legally
due date this amount is known as Bankers Discount
vi.Thus , B.D is the S.I on the face for the period from the date
on which the bill was discounted and the legally due date
vii.Bankers Gain (B.G) = (B.D) – (T.D) for the unexpired time
Note:
When the date of the bill is not given,grace days are not to be added
Formulae:
(1)B.D = S.I on bill for unexpired time
(2)B.G = (B.D) – (T.D) = S.I on T.D = (T.D)^2 /P.W
(3)T.D = sqrt(P.W * B.G)
(4)B.D = (Amount * Rate * Time)/100
(5)T.D = (Amount * Rate * Time)/(100+(Rate * time)
(6)Amount = (B.D * T.D)/(B.D – T.D)
(7)T.D = (B.G * 100)/(Rate * Time)
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Simple Problems
1.If the true discount on a certain sum due 6 months hence at
15% is Rs 120.What is the bankers discount on the same for same
time and the same rate.
Sol:- B.G = S.I on T.D
= RS (120 * 15 * ½ * 1/100)
= 9
(B.D) – (T.D) = 9
B.D = 120 + 9 =129
2.The bankers discount on Rs 1800 at 12 % per annum is equal to the
true discount on Rs 1872 for the same time at the same rate .Find
the time.
Sol:- S.I on Rs 1800 = T.D on Rs 1872
P.W of Rs 1872 is Rs 1800
Rs 72 is S.I on Rs 1800 at 12%
Time = (100 * 72)/(12 * 1800)
= 1/3 years = 4 months
3.The bankers discount and true discount on a sum of money due 8 months
hence are Rs.120 & Rs.110 resp. Find the sum & the rate per cent
Sol:- Sum = (B.D * T.D) / (B.D) – (T.D)
= (120 * 110) / (120 – 110)
= 1320
Since B.D is S.I on sum due, so S.I on Rs 1320 for 8 months is
Rs 120
Rate = (100 * 120) / (1320 * 2/3)
= 13 7/11%
Medium Problems
1.The Bankers discount on Rs 1650 due a certain time hence is Rs 165.
find the true discount and the bankers gain.
Sol :- Sum = (B.D * T.D) / (B.D – T.D)
= (B.D * T.D) / B.G
T.D/B.G = Sum/B.D =650/165 =10/1
Thus if B.G is Rs 1 ,T.D = Rs 10
if B.D is Rs 11 ,T.D = Rs 10
if B.D is Rs 165,T.D = Rs (10/11 * 165) = 150
B.G =Rs(165 – 150) = Rs 15
2.The Present worth of a bill due something hence is Rs 1110 and the
true discount on the bill is Rs.110 . Find the bankes discount & the
bankers gain.
Sol:- T.D = sqrt (P.W * B.G)
B.G = (T.D)^2 /P.W
= (110 * 110) / 1110
= 11
B.D = (T.D + B.G)
= (110 + 11)
= Rs 121
3.What rate percent does a man get for his money when in discounting
Sol:- Let the amount of the bill =100
Money deducted = 10
Money received by the holder of the bill = (100 – 10)
= 90
S.I on Rs 90 for 10 months = 10
Rate = (100 * 10) / (90 * 10/12)
= 13 1/3%
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Complex Problems
1.A bill for Rs.6000 is drawn on July 14 at 5 months . It is
discounted on 5th October at 10%.Find the bankers discount
true discount, bankers gain and the money that the holder of
the bill receives.
Sol:-
Face value of the bill = Rs.6000
date on which the bill was drawn = July 14 at 5 months
nominally due date = December 14
legally due date = December 17
Date on which the bill was discounted = October 5
Unexpired time : Oct Nov Dec
26 + 30 + 17 = 73days =1/5 years
B.D = S.I on Rs 6000 for 1/5 year
= Rs (6000 * 10 * 1/5 * 1/100) = Rs 120
T.D = Rs(6000 * 10 *1/5)/(100 + (10 * 1/5))
= Rs. 117.64
B.G = (B.D) – (T.D)
= Rs(120 -117.64)
= Rs 2.36
Money received by the holder of the bill
= Rs(6000 – 120) = 5880
2. The bankers gain on a certain sum due 1 ½ year hence
is 3/25 of the bankers discount .The rate percent is
Sol:- Let B.D = 1 then B.G = 3/25
T.D = (B.D – B.G)
= (1 – 3/25)
= 22/25
sum = (1 * 22/25) / (1 – 22/25)
= 22/3
S.I on Rs 22/3 for 1 ½ year is 1.
Rate = (100 * 1) / (22/3 * 3/2)
= 9 1/9%
3. The bankers gain of a certain sum due 2 years hence
at 10% per annum is Rs 24 .The percent worth is
Sol:-
T.D = (B.G * 100) / (Rate * Time)
00) / (10 * 2)
= 120.
P.W = (100 *T.D) / (Rate * Time)
= (100 * 120) /(10 * 2)
= 600
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