## 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. Rs. 800
2. Rs. 650
3. Rs. 750
4. Rs. 850

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 bill for Rs. 2520 due 6 months hence at 10 % per annum is :
1. Rs. 180
2. Rs. 140
3. Rs. 80
4. Rs. 120

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 true discount on a bill of Rs. 2160 is Rs. 360. What is the banker’s discount?
1. Rs. 432
2. Rs. 422
3. Rs. 412
4. Rs. 442

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 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. Rs. 248
2. Rs. 278
3. Rs. 228
4. Rs. 258

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 banker’s discount on a bill due 4 months hence at 15 % is Rs. 420. What is the true discount?
1. Rs. 410
2. Rs. 400
3. Rs. 390
4. Rs. 380

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