## Discount

#### Discount

1. A bill is discounted at 5 % per annum. If banker’s discount be allowed, at what rate of interest must the proceeds be invested, so that nothing is lost?
1. 5%
2.  4 19 % 20

3.  5 5 % 9

4. 10%

1. Let the sum be \$ 100.
Then, B.D. = \$ 5 Proceeds = \$ (100 - 5) = \$ 95
∴ \$ 5 must be the interest on \$ 95 for 1 year.

##### Correct Option: C

Let the sum be \$ 100.
Then, B.D. = \$ 5 Proceeds = \$ (100 - 5) = \$ 95
∴ \$ 5 must be the interest on \$ 95 for 1 year.

 So, rate = 100 x 5 = 5 5 % 95 x 1 19

1. A owes B \$ 1350 due in 3 months and B owes A \$ 1078 due 5 months. If they agrees to settle their account right now at 5 % p.a, A should pay to B :
1.  \$ 277 1 3
2. \$ 288.25
3. \$ 302
4. None of these

1. According to question , we have

 P.W. of \$ 1350 = 1350 x 100 = 1350 x 400 = \$ 1,333.33 100 + [ ( 3 / 12 ) x 5 ] 405

##### Correct Option: A

According to question , we have

 P.W. of \$ 1350 = 1350 x 100 = 1350 x 400 = \$ 1,333.33 100 + [ ( 3 / 12 ) x 5 ] 405

 P.W. of \$ 1078 = 1078 x 100 = 1078 x 1200 = \$ 1056 100 + [ ( 5 / 12 ) x 5 ] 1225

 ∴ A should pay B = \$ 4000 - 1056 3

 A should pay B = \$ 832 = \$ 277 1 3 3

1. The B.G. on a sum due 3 years at 10 % is \$ 180. The B.D. is :
1. \$ 680
2. \$ 780
3. \$ 580
4. \$ 480

1. Here , Rate = 10% , Time = 3 years , B.G. = \$ 180

 T.D. = B.G. x 100 = \$ 180 x 100 = \$ 600 R x T 10 x 3

##### Correct Option: B

Here , Rate = 10% , Time = 3 years , B.G. = \$ 180

 T.D. = B.G. x 100 = \$ 180 x 100 = \$ 600 R x T 10 x 3

∴ Banker 's Discount ( B.D. ) = True discount + Banker 's Gain ( B.G. )
Banker 's Discount ( B.D. ) = \$ (600 + 180) = \$ 780.

1. The banker’s gain on a certain sum due in 2 years at 5 % per annum is \$ 8. The present worth is :
1. \$ 800
2. \$ 1600
3. \$ 1200
4. \$ 880

1. Given :- Banker 's Gain = \$ 8 , Rate = 5% , Time = 2 years

 True Discount = B.G. x 100 = \$ 8 x 100 Rate x Time 5 x 2

##### Correct Option: A

Given :- Banker 's Gain = \$ 8 , Rate = 5% , Time = 2 years

 True Discount = B.G. x 100 = \$ 8 x 100 Rate x Time 5 x 2

True Discount = \$ 800

1. The B.G. on a certain sum due in 5 years is 3/23 of B.D. Here, the rate of interest is :
1. 6%
2. 5%
3. 4%
4. 3%

1. Let, Banker 's Discount = \$ 1

 ∵ Banker 's Gain = \$ 3 23

∴ True Discount = Banker 's Discount - Banker 's Gain
 True Discount = \$ 1 - 3 = \$ 20 23 23

##### Correct Option: D

Let, Banker 's Discount = \$ 1

 ∵ Banker 's Gain = \$ 3 23

∴ True Discount = Banker 's Discount - Banker 's Gain
 True Discount = \$ 1 - 3 = \$ 20 23 23

 ∴ Sum = B.D. x T.D. B.D. -T.D.

 Sum = 1 x 20 = \$ 23 20 1 - 20 3 23

 ∵ S.I. on \$ 20 for 5 years is \$ 1 3

 ∴ Rate of interest = 100 x 3 = 3 % 20 x 5