Banker's Discount Problems, Formula And Solution

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.

Getting Started

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.

Now,

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:

Example 1

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.

Solution:

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

Example 2

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?

Solution:

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

Example 3

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.

Solution

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

Example 4

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.

Solution

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:

Question 1

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

Solution: (b)

Explanation

P.W. = Rs. (440 – 80) = Rs. 360

Therefore, S.I. on Rs. 360 = Rs. 80

S.I. on Rs. 440 = [(80 / 360) * 440] = Rs. 97.77

Hence, B.D. = Rs. 98

Question 2

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

Solution: (b)

Explanation

B.G. = (T.D.)² / P.W. = Rs. [(40 * 40) / 900] = Rs. 1.77

Hence, B.D. = (T.D. + B.G.) = Rs. (40 + 1.77) = Rs. 41.77

Question 3

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

Solution: (c)

Explanation

B.G = (T.D.)²/P.W

= Rs [(150*150)/1500] = Rs 15

Question 4

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

Solution: (a)

Explanation

T.D. = [B.G. * 100] / [Rate * Time] = Rs. [30 * 100] / [10 * 2.5] = Rs. 120

Hence, P.W. = [100 * T.D.] / [Rate * Time] = Rs. [100 * 120] / [10 * 2.5] = Rs.480

Question 5

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

Solution: (d)

Explanation

T.D. = [B.G. * 100] / [Rate * Time] = Rs. [5 * 100] / [10 * 1] = Rs. 50

Question 6

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

Solution: (a)

Explanation

T.D. = [B.D. * 100] / [100 + (R * T)] = Rs. [450 * 100] / [100 + (12 * 1 / 2)]

= Rs. [450 * 100] / 106 = Rs. 424.52

Question 7

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

Solution: (c)

Explanation

T.D. = [B.G. * 100] / [R * T] = Rs. [300 * 100] / [10 * 3]

= Rs. 1000

Hence, B.D. = Rs. (1000 + 300) = Rs.1300

Question 8

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

Solution: (d)

Explanation

T.D. = √P.W. x B.G.

= √361 * 25 = 95

Question 9

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

Solution: (b)

Explanation

S.I. on Rs. 1500 = T.D. on Rs. 1550

Hence, Rs. 1500 is the P.W. of Rs. 1550

So, 1550 – 1500 = Rs. 50

i.e Rs. 80 is S.I. on Rs. 1500 at 10%

Hence, Time = [100 * 50] / [1500 * 10] years = 1/3 yr = 4 months

Question 10

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

a. 71%
b. 85%
c. 25%
d. 15%

Solution: (a)

Explanation

B.D. for 5/2 years = Rs. 650

B.D. for 3 yrs = Rs. (650 * 2 / 5 * 3) = Rs. 780

T.D. for 3 yrs = Rs. 700

Hence, Sum = [B.D. * T.D.] / [B.D. – T.D.] = Rs. [780 * 700] / 80 = Rs. 6825

Thus, Rs. 780 is S.I. on Rs. 6825 for 3 yrs

Hence, Rate = [100 * 780] / [ 6825 * 2] % = 5.71%

Question 11

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

Solution: (a)

Explanation

Sum = [B.D. * T.D.] / [B.D. – T.D.]

= Rs. [50 * 40] / [50 – 40]

= Rs. [60 * 45] / 15 = Rs. 200

Question 12

The bankers discount (B.D) on a certain sum due 2 years later is 13/10 times the true discount. Find the rate percentage
a. 11%
b. 10%
c. 5%
d. 5%

Solution: (c)

Explanation

Let T.D. be Re 1.

Then, B.D. = Rs 13 / 10 = Rs. 1.30

Hence, Sum = Rs [1.30 * 1] / [ 1.30 – 1]

=> Rs. [130 / 30] = Rs 4.30

Hence, S.I. on Rs 4.30 for 2 years is Rs. 1.30

Hence, Rate = [100 * 1.30] / [4.30 * 2] % = 15.11%

Question 13

The bankers gain on a certain sum due 2 ½ yrs hence is 7/25 of the bankers discount. The rate percent is
a. 15.55%
b. 18.55%
c. 16.25%
d. 14.25%

Solution: (a)

Explanation

Let B.D = Re. 1

Then, B.G. = Re (7 / 25)

Hence, T.D. = (B.D. – B.G.) = Re. [1 – (7 / 25)]

= Re. 18 / 25

Sum = [1 * (18 / 25)] / [1 – (18 / 25)] = Re (18 / 7)

S.I. on Rs. (18 / 7) for 2½ years is Re. 1

Hence, Rate = [100 * 1] / [(18 / 7) * (5 / 2)] % = [140 / 9]%

= 15.55 %

Question 14

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

Solution: (b)

Explanation:

P.W. = 1500
T.D. = 150
Sum due = P.W. + T.D. = 1500 + 150 = 1650
T.D. is the interest on the P.W.
Now, interest on 1500 is 150
Banker’s discount = Interest on the sum due.
Interest on 1650 = 150 / 1500 * 1650 = Rs. 165
So, banker’s discount = Rs. 165
Banker’s gain = banker’s discount – true discount
= 165 – 150 = 15

Question 15

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

Solution: (b)

Explanation:

T. D. = √P.W. × B.G.

Therefore, B.G. = ((T.D.)² / P.W.)

= Rs. (120 × 120 / 1200 = Rs. 12

So, B.D. = (T.D. + B.G.) = Rs. (120 + 12) = Rs. 132

Question 16

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

Solution: (c)

Explanation:

Sum = (B.D. x T.D.) / (B.D. – T.D.)

= (B.D. x T.D.) / B.G.

So, T.D. / B.G. = Sum / B.D. = 1450 / 145 = 10 / 1

i.e., if B.G. is Re. 1, T.D. = Rs. 10

B.D. = Rs. 10 + 1 = 11

So, if B.D. is Rs. 11, T.D. = Rs. 10

If B.D. is Rs. 145, T.D. = Rs. (10 / 11) x 145 = Rs. 131.81

Also, B.G. = Rs. (145 – 131.81) = Rs. 13.18

Question 17

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 %

Solution: (c)

Explanation:

Let the amount of bill be Rs. 100

Money deducted = Rs. 5

Money received by the bill holder = Rs. (100 – 5) = Rs. 95

S.I. on Rs. 95 for 8 months = Rs. 5

Rate = [(100 x 5 x 8) / (95 x 5)] = 8.42%

Question 18

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%

Solution: (a)

Explanation:

Sum = (B.D. * T.D.) / (B.D. – T.D.)

= (240 * 230) / (240 – 230)

So, the required sum = 55200 / 10 = Rs. 5520

As B.D. is the S.I. on sum due,

So S.I. on Rs. 5520 for 8 months is Rs. 240.

S.I. = Amount * rate of interest * time

240 = 5520 * r * (8 / 12)

240 = 5520 * (r / 100) * (2 / 3)

r = (240 * 100 * 3) / (5520 * 2)
= 6.52 %

Question 19

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

Solution:(a)

Explanation:

T.D = [B.G. * 100] / [R * T]

= (9 * 100) / (15 * 1)

= 900 / 15 = Rs. 60

Question 20

The bankers gain on a sum due 3 years hence at 15% per annum is Rs. 270. What is the banker’s discount?
a. 780
b. 870
c. 580
d. 480

Solution: (b)

Explanation:

T.D = [B.G * 100] / [R * T]

= [270 * 100] / [15 * 3] = Rs. 600

B.G. = Bankers discount – True discount
B.D. = B.G. + True discount
= 270 + 600
= Rs. 870

Question 21

The B.G. on a certain sum 2 years hence at 10% is Rs. 500. Find the present worth.
a. 12500
b. 10500
c. 11000
d. 11500

Solution: (a)

Explanation:

T.D. = [B.G. * 100] / [R * T]

= [500 * 100] / [10 * 2] = Rs. 2500

T.D = √P.W. * B.G

2500 = √P.W. * 500

6250000 = P.W. * 500

P.W. = 6250000 / 500

= Rs. 12500

Question 22

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

Solution: (b)

Explanation:

P.W. = Rs. (600 – 40) = Rs. 560

S.I. on Rs. 560 = Rs. 40

S.I. on Rs. 560 = Rs.( 40 / 560) x 600 = Rs. 42.85

B.D. = Rs. 42.85

Question 23

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

Solution: (d)

Explanation:

B.G = (T.D.)² / P.W.

= (25)² / 550

= Rs 1.13

B.G. = B.D. – T.D.
1.13 = B.D. – 25
B.D. = 1.13 + 25 = Rs. 26.13

Tutorialwing

Banker’s Discount Problems, Formula And Solution

Getting Started

Section A: (Terms & Formulas)

Important Formulas Related to Banker’s Discount –

Section B: (Examples)

Example 1

Example 2

Example 3

Example 4

Section C: (Multiple choice questions)

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

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Getting Started

Section A: (Terms & Formulas)

Important Formulas Related to Banker’s Discount –

Section B: (Examples)

Example 1

Example 2

Example 3

Example 4

Section C: (Multiple choice questions)

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

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