Banker's Discount
-> Suppose a merchant A buys goods worth Rs.10000 from another merchant B at a credit of say 5 months
-> Then,B prepares a bill , called the bill of exchange
-> 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
-> Three days (grace days) are added to it get a date known as legally due date
-> 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
-> 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
-> 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)
BASIC PROBLEM
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%
-> Suppose a merchant A buys goods worth Rs.10000 from another merchant B at a credit of say 5 months
-> Then,B prepares a bill , called the bill of exchange
-> 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
-> Three days (grace days) are added to it get a date known as legally due date
-> 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
-> 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
-> 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)
BASIC PROBLEM
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%
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