## Banker's Discount

#### Banker's Discount

1. The banker's gain on a bill due 2 years hence at 5% is Rs. 8, find the present worth of the bill ?

1. P.W. = [8 x 100 x 100] / [10 x 10]

##### Correct Option: A

P.W. = [8 x 100 x 100] / [10 x 10]
= Rs. 800

1. The true discount on a certain sum due 6 months hence at 15 % is Rs. 240. What is the banker’s discount on the same sum for the same time at the same rate?

1. Given in the question,
True Discount = 240
Rate of interest = 15%
Time = 6 months = 1/2 year
As we know the formula ,

 True Discount = Banker's Gain × 100 Time in years x Rate of Interest

 ⇒ 240 = Banker's Gain × 100 (1/2 × 15)

##### Correct Option: D

Given in the question,
True Discount = 240
Rate of interest = 15%
Time = 6 months = 1/2 year
As we know the formula ,

 True Discount = Banker's Gain × 100 Time in years x Rate of Interest

 ⇒ 240 = Banker's Gain × 100 (1/2 × 15)

 ⇒ 240 = Banker's Gain × 100 x 2 (1 × 15)

 ⇒ 24 = Banker's Gain × 10 x 2 (1 × 15)

 ⇒ 24 = Banker's Gain × 2 x 2 (1 × 3 )

 ⇒ 6 = Banker's Gain × 1 3

⇒ Banker's Gain = Rs. 6 x 3
⇒ Banker's Gain = Rs. 18
Apply the formula, As we know that ,
Banker's Gain = Banker's Discount − True Discount
⇒ 18 = Banker's Discount − 240
⇒ Banker's Discount = Rs. 258

1. The true discount on a bill of Rs. 2160 is Rs. 360. What is the banker’s discount?

1. True Discount is the Simple Interest on the present value for unexpired time
⇒ Simple Interest on Rs. 1800 for unexpired time = Rs. 360
Banker’s Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2160 for unexpired time

 = 360 × 2160 1800

##### Correct Option: A

True Discount is the Simple Interest on the present value for unexpired time
⇒ Simple Interest on Rs. 1800 for unexpired time = Rs. 360
Banker’s Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2160 for unexpired time

 = 360 × 2160 1800

 = 1 × 2160 = Rs. 432 5

1. The true discount on a bill for Rs. 2520 due 6 months hence at 10 % per annum is :

1. Given in the question,
Face Value = 2520;
Time = 6 months = 1/2 year
Rate of interest = 10 %
As we know the formula,
True Discount = Face Value x ( Rate of Interest x Time in years ) / ( 100 + Rate of interest x Time )

⇒ True Discount = 2520 x (10 x 1/2 ) / (100 + (10 x 1/2 ))

##### Correct Option: D

Given in the question,
Face Value = 2520;
Time = 6 months = 1/2 year
Rate of interest = 10 %
As we know the formula,
True Discount = Face Value x ( Rate of Interest x Time in years ) / ( 100 + Rate of interest x Time )

⇒ True Discount = 2520 x (10 x 1/2 ) / (100 + (10 x 1/2 ))
⇒ True Discount = 2520 x ( 5 ) / (100 + ( 5 ))
⇒ True Discount = 2520 x 5 /105
⇒ True Discount = 2520 / 21
⇒ True Discount = Rs. 120

1. The banker’s discount on a bill due 4 months hence at 15 % is Rs. 420. What is the true discount?

1. Given in the question,
Banker's Discount = 420
Time in years = 6 months = 1/2 years
Rate of interest = 15 %
As we know the formula,
True Discount = Banker's Discount × 100 (100 + Time in years x Rate of interest )

True Discount = 420 × 100 (100 + 4/12 × 15)

##### Correct Option: B

Given in the question,
Banker's Discount = 420
Time in years = 4 months = 4/12 years = 1/3 years
Rate of interest = 15 %
As we know the formula,
True Discount = Banker's Discount × 100 (100 + Time in years x Rate of interest )

True Discount = 420 × 100 (100 + 4/12 × 15) ( 12 Months = 1 Year)
= 420 × 100 (100 + 5) = 400