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. View Hint View Answer Discuss in Forum

    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. View Hint View Answer Discuss in Forum

    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. View Hint View Answer Discuss in Forum

    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. View Hint View Answer Discuss in Forum

    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. View Hint View Answer Discuss in Forum

    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