## Banker's Discount

#### Banker's Discount

1. The present worth of a certain bill due sometime hence is Rs. 1600 and true discount on the bill is Rs. 160. Find the banker's discount and the extra gain the gain banker would make in the transaction ?
1. Rs. 176, Rs. 18
2. Rs. 186, Rs. 16
3. Rs. 176, Rs. 16
4. None of these

1. 160 = √1600 x B.G.
∴ B.G. = (160 x 160)/1600 = Rs. 16

##### Correct Option: C

160 = √1600 x B.G.
∴ B.G. = (160 x 160)/1600 = Rs. 16
∴ Banker's discount = 160 + 16 = Rs. 176
[∵ B.D. = T.D. + B.G.]

1. The holder of a bill for Rs. 17850 nominally due on 21st May, 1991 received Rs. 357 less than the amount of the bill by having it discounted at 5%. When was it discounted ?
1. December 29, 1990
2. December 30, 1989
3. December 19, 1990
4. None of these

1. Clearly S.I. on Rs. 17850 at 5% is Rs. 357.
∴ Time = (100 x 357) / (17850 x 5) = 2/5 = 146 days
So, the bill is 146 days prior to 24th May, the legally due date
May, April, March, Feb., Jan.,Dec.,
= 24 + 30 + 31 + 28 + 31 + 2 = 146 days

##### Correct Option: A

Clearly S.I. on Rs. 17850 at 5% is Rs. 357.
∴ Time = (100 x 357) / (17850 x 5) = 2/5 = 146 days
So, the bill is 146 days prior to 24th May, the legally due date
May, April, March, Feb., Jan.,Dec.,
= 24 + 30 + 31 + 28 + 31 + 2 = 146 days
So, the bill was discounted on 29 Dec. 1990.

1. A bill is discounted at 5% per annum. If banker's discount be allowed, at what rate per cent must the proceeds be invested, so that nothing may be lost ?
1. 5%
2. 419/21%
3. 55/19%
4. 10%

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

##### Correct Option: C

Let the sum be Rs. 100. Then, B.D = Rs. 5.
Proceeds = Rs. (100 - 5) = Rs. 95.
∴ Rs. 5 must be the interest on Rs. 95 for 1 year.
So, rate = (100 x 5) / (95 x 1) = 55/19%

1. A bill for ₹ 10200 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's discount, true discount. banker's gain and the money that the holder of the bill receives ?
1. ₹ 204 , ₹ 200, ₹ 4 and ₹ 9996
2. ₹ 100 , ₹ 200, ₹ 2 and ₹ 4989
3. ₹ 121 , ₹ 172, ₹ 132 and ₹ 4046
4. None of these

1. Face value of the bill = ₹ 10200
Date on which the bill was drawn = July 14 at 5 Months
Nominally due date = Dec. 14
Legally due date = Dec. 17
Date on which the bill was discounted = Oct. 05
Unexpired time
Oct.-26, Nov. - 30, Dec - 17 = 73 days = 73/365 yr = 1/5 yr

∴ BD = SI on ₹ 10200 for 1/5 yr
= (10200 x (10/100) x 1/5)
= ₹ 204

TD = [10200 x (1/5) x 10] / [100 + 10 x (1/5)]
= (10200 x 2)/102 = ₹ 200
BG = (BD) - (TD) = (204 - 200) = ₹ 4

##### Correct Option: A

Face value of the bill = ₹ 10200
Date on which the bill was drawn = July 14 at 5 Months
Nominally due date = Dec. 14
Legally due date = Dec. 17
Date on which the bill was discounted = Oct. 05
Unexpired time
Oct.-26, Nov. - 30, Dec - 17 = 73 days = 73/365 yr = 1/5 yr

∴ BD = SI on ₹ 10200 for 1/5 yr
= (10200 x (10/100) x 1/5)
= ₹ 204

TD = [10200 x (1/5) x 10] / [100 + 10 x (1/5)]
= (10200 x 2)/102 = ₹ 200
BG = (BD) - (TD) = (204 - 200) = ₹ 4

Money received by the holder of the bill = ₹ (10200 - 204) = ₹ 9996

1. The banker's discount on a certain sum due 4 yr, hence is 11/10 of the true discount. Find the rate per cent per annum.
1. 2.5%
2. 5%
3. 5.5%
4. 1.5%

1. Let TD = N, then BD = 11N/10
Sum = (BD x TD) / (BD - TD) = [(11N/10) x N] / [11N/10 - N]
= [11N2/10] / [N/10] = 11N
SI on ₹ 11N for 4 yr is ₹ 11N/10.
∴ Rate = (100 x 11N/10)/(11N x 4)% per annum

##### Correct Option: A

Let TD = N, then BD = 11N/10
Sum = (BD x TD) / (BD - TD) = [(11N/10) x N] / [11N/10 - N]
= [11N2/10] / [N/10] = 11N
SI on ₹ 11N for 4 yr is ₹ 11N/10.
∴ Rate = (100 x 11N/10)/(11N x 4)% per annum
= 2.5% per annum