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In this post, we will be learning about Banker’s Discount questions and answers. We will see many aptitude questions and answers on the topic Bankers Discount with tricks/shortcuts to solve them.
So, let’s start the learning now.
This post contains three sections –
- Section A – This section contains important formulas, short tricks, concepts on Bankers Discount.
- Section B – This section contains some examples that demonstrate how to solve questions on Bankers Discount using short tricks, formulas shown in section A.
- Section C – Go to this section to solve some problems on Bankers Discount.
Where to start from?
We recommend go through section A, then section B, then section C. Even if you are familiar with this topic, do not just skip section A and section B.
Section A: (Terms & Formulas)
Let’s first go through some important concepts –
- Bill of exchange – If tom gets money worth Rs 20000 from Vicky at a credit of say 5 months at a rate of 5% interest, Then, Vicky will prepare a bill called the bill of exchange. Tom will sign this bill to allow Vicky to withdraw the money from his account after 5 months.
- Nominally due date – The date exactly on the agreed period of bill of exchange is the nominally due date. In the ex above, it is the date exactly after 5 months.
- Legally due date – Nominal due date + 3 days grace period. Bill is allowed to be presented to the bank on or after the legally due date.
- Bankers Gain (B.G) = Bankers Discount (B.D) – (T.D) for the unexpired time
- Present Value: The amount of money to be paid before the agreed due date to clear off debt is called present worth.
For example: If Tom plans to repay the money in 2.5 months instead of waiting upto 5 months, the remaining payment would be the present worth.
- True Discount: The true discount is the difference between the sum due at the end of the given time and its present worth. So, in the above example, true discount = Face value (sum due) – Present value = 20000 – 19510.23 = 489.77
In other words, the true discount is the simple interest on the present value or worth for the unexpired time. In other words, the present value or present worth of a sum of money due at the end of a specified time is that sum which will amount to the sum due with its interest calculated for the given time at the given rate of interest.
So, if the bank pays Rs. 19510.23 (present worth) to Tom in exchange for the bill, the bank would not make a profit from this deal. Hence, the bank does not use true discount for its use. It would calculate the discount with a different formula called Banker’s Discount.
- Banker’s Discount = FV * r * t = 20000 * 0.05 * (½) = 500
So, instead of discounting true discount, the Banker will discount the banker’s discount from the face value to do the pays out
= Rs. 20000 – 500 = Rs.19500
So, Banker’s Gain = Present Value of the Note – Actual Payout = 1.23
= (Face Value – True Discount) – (Face Value – Banker’s Discount)
B.G. = Banker’s discount – True Discount = 500 – 489.77 = 10.23
Bankers Discount (B.D) In the case the Vicky wants to have the money returned before the legally due date, Then he need to have the money from the banker or broker who will calculate S.I (Simple interest) on the face value (i.e 20000 in this ex) for the period from the date the bill was discounted and the legally due date. This is called as Bankers Discount. (B.D)
Thus bankers discount is the SI on the face value for the period from the date on which the bill was discounted and the legally due date.
Note: If the date of the bill is not provided, grace days are not to be added.
Now, it’s time to go through some important formulas relate to bankers discount –
Important Formulas Related to Banker’s Discount –
Let F = Face Value of the Bill, T.D. = True Discount, B.D. = Bankers Discount, B.G. = Banker’s Gain, R = Rate of Interest, P.W. = True Present Worth and T = Time in Years
- B.D. = S.I. on bill for unexpired time.
- B.G. = (B.D.) – (T.D.) = S.I. on T.D. = (T.D.)² / P.W.
- T.D. = √P.W. x B.G.
- B.D = [Amount x Rate x Time] / 100
- T.D. = [Amount x Rate x Time] / [100 + (Rate x Time)]
- Amount =[B.D x T.D] / [B.D – T.D]
- T.D = [B.G x 100] / [Rate * Time]
Section B: (Examples)
Now, we will see how to approach any questions on Bankers Discount and looking at what are the key factors we should look into before trying to solve these questions. Please do not move to next section without going through each of the Bankers discount example problems below:
A bill for Rs 4000 is drawn on June 14 at 5 months. It is discounted on 5th September at the rate of 10. Find the bankers discount, true discount, bankers gain and the money that the holder of the bill receives.
Face value of the bill = Rs 4000/-
Date on which the bill was drawn = June 14 at 5 months
Nominally due date = Nov 14
Legally due date = Nov 17
Date on which the bill was discounted = September 5
Unexpired time: Sep Oct Nov
25 + 31 + 17 = 73 days = 1/5 Year
Therefore, B.D = S.I on Rs 4000 for1/5 yr
= Rs [4000*10*(1/5)*(1/100)] = Rs 80
T.D = Rs [4000*10*(1/5)] / [100+ (10*1/5)] = Rs 8000/102 = Rs 78.43
Therefore, B.G =(B.D) – (T.D) = Rs (80 -78.43) = Rs 1.56
Money Received by the holder of the bill = Rs (4000-80) = Rs 3920
If the true discount on a sum of money due 6 months hence at the rate of 10% is Rs 300, what is the bankers discount on the same for the same time and at the same rate?
B.G = S.I on T.D
= Rs [30 * 10 * (1/2) * ( 1/100) ] = Rs 1.5
Therefore, (B.D) – (T.D) = Rs 1.5
B.D = 1.5 + T.D = 1.5 + 300 = 301.5 Rs
The bankers discount on Rs 1500/- at 10 % per annum is equal to the true discount on Rs 1800 for the same time at the same rate. Find the time.
S.I on Rs 1500 = T.D on Rs 1800
Therefore, P.W of Rs 1800 is 1500
Rs 300 (1800 -1500) is S.I on Rs 1500 at 10%
Hence Time = [(100*300)] /[(10*1500)] year = 2 years
The Bankers discount and the True discount on a sum of amount which is 8 months due are Rs 150 and 140 respectively. Find the sum and the percentage of rate.
Sum = [(B.D*T.D) / (B.D – T.D)] = Rs [(150*140) /(150 – 140)] = Rs 2100
Since B.D is S.I on sum due, so S.I on Rs 2100 for 6 months is Rs 150
Therefore, Rate = [100*150]/[2100*(2/3)] % = 10.71 %
Section C: (Multiple choice questions)
In this section, we will see different mcq’s on Bankers Discount (with short tricks, if available).
Mark against the correct answer:
The true discount on a bill of Rs 440 is Rs 80. The bankers discount is :
a. Rs 60
b. Rs 98
c. Rs 110
d. Rs 112
The present worth of a certain bill due after a period of time is Rs 900 and the true discount is Rs 40. The bankers discount is:
a. Rs. 41
b. Rs. 41.77
c. Rs. 39.38
d. Rs. 40.98
The present worth of a certain sum due after a period of time is Rs 1500 and the true discount is Rs 150. The bankers gain is:
a. Rs. 20
b. Rs. 24
c. Rs. 15
d. Rs. 12
The banker’s gain of a certain sum due 2.5 years hence at a rate of 10% per annum is Rs 30. The present worth is:
a. Rs. 480
b. Rs. 520
c. Rs. 600
d. Rs. 960
The bankers gain (B.G.) on a bill due 1 year hence at a rate of 10% per annum is Rs 5. The true discount is:
a. Rs. 72
b. Rs. 36
c. Rs. 54
d. Rs. 50
The bankers discount on a bill due 6 months hence at 12% is Rs. 450. The true discount is:
a. Rs. 424.52
b. Rs. 360.25
c. Rs. 480.48
d. Rs. 320.47
The bankers gain on a sum due 3 years hence at 10% per annum is Rs. 300. The bankers discount is
a. Rs. 1130
b. Rs. 1030
c. Rs. 1300
d. Rs. 1205
The present worth (P.W.) of a sum due for a period of time is Rs 361 and the bankers gain is Rs. 25. The true discount is:
a. Rs 94
b. Rs 98
c. Rs 96
d. Rs 95
The bankers discount on Rs 1500 at 10% per annum is the same as true discount on Rs. 1550 for the same time and at the same rate. The time is
a. 3 months
b. 4 months
c. 6 months
d. 8 months
The bankers discount on a sum of money for 2 ½ years is Rs. 650 and the true discount on the same sum for 3 years is Rs 700. The rate percent is
The banker’s discount of a certain sum of money is Rs 50 and the true discount on the same sum for the same time is Rs 40. The sum due is
a. Rs 200
b. Rs 420
c. Rs 540
d. Rs 550
The bankers discount (B.D) on a certain sum due 2 years later is 13/10 times the true discount. Find the rate percentage
The bankers gain on a certain sum due 2 ½ yrs hence is 7/25 of the bankers discount. The rate percent is
The present worth or value of a bill due sometime hence is Rs. 1500 and the true discount is Rs. 150. Solve to find the banker’s discount and the banker’s gain.
a. 132 , 16
b. 165 , 15
c. 131 , 14
d. 121 , 11
The present worth (P.W) of a bill due sometime later is Rs 1200 and the true discount (T.D) on the bill is Rs 120. Solve to find the bankers discount and the bankers gain
a. Rs. 121
b. Rs. 132
c. Rs. 120
d. Rs. 130
The bankers discount on Rs 1450 due a certain time hence is Rs 145. Find the true discount and the bankers gain
a. Rs 150.25, Rs 15.52
b. Rs 110.45, Rs 11.54
c. Rs 131.81, Rs 13.18
d. Rs 140.12, Rs 14.21
When in discounting a bill due 8 months hence; Determine the rate percent a man gets for his money when Rs 5 is deducted from the amount of the bill?
a. 5.25 %
b. 6.25 %
c. 8.42 %
d. 7.25 %
The banker’s discount (B.D) and the true discount (T.D) on a sum of money due 8 months hence are 240 and 230 respectively. What are the sum and the rate percent?
a. 5520, 6.52%
b. 5620 , 12.5%
c. 5420 , 10.5%
d. 5720 , 9.5%
If the banker’s gain on a bill due one year hence at 15% per annum is Rs. 9, what is the true discount?
a. Rs 60
b. Rs 65
c. Rs 70
d. Rs 75
The bankers gain on a sum due 3 years hence at 15% per annum is Rs. 270. What is the banker’s discount?
The B.G. on a certain sum 2 years hence at 10% is Rs. 500. Find the present worth.
The true discount (T.D) on a bill of Rs. 600 is Rs. 40. The banker’s discount(B.D) is:
a. Rs 60.56
b. Rs. 42.85.
c. Rs 110.34
d. Rs 112.25
The present worth of a certain bill due sometime hence is Rs. 550. If the true discount is Rs. 25, what is the banker’s discount?
a. Rs. 12.5
b. Rs. 13.5
c. Rs. 14.5
d. Rs. 15.5