Bankers Discounts

Formulae: 

 

i. Suppose a merchant A buys goods worth Rs.10000 from another    

merchant B at a credit of say 5 months

 

ii.Then,B prepares a bill , called the bill of exchange 

 

iii. A signs this bill & allows B to withdraw the amount from his

bank account after exactly 5 months,the date exactly after 

5 months is called Nominally due date

 

iv. Three days (grace days) are added to it get a date known as

legally due date

 

v.Suppose B wants to have money before legally due date then he 

can have the money from banker or a broker who deducts S.I on the 

face value (i.e., 10000) for the period from the date on which 

the bill was discounted (i.e paied by the banker) & the legally 

due date this amount is known as Bankers Discount

 

vi.Thus , B.D is the S.I on the face for the period from the date 

on which the bill was discounted and the legally due date

 

vii.Bankers Gain (B.G) = (B.D) – (T.D) for the unexpired time

 

Note:

When the date of the bill is not given,grace days are not to be added

 

Formulae:

 

(1)B.D = S.I on bill for unexpired time

(2)B.G = (B.D) – (T.D) = S.I on T.D = (T.D)^2 /P.W

(3)T.D = sqrt(P.W * B.G)

(4)B.D = (Amount * Rate * Time)/100

(5)T.D = (Amount * Rate * Time)/(100+(Rate * time)

(6)Amount = (B.D * T.D)/(B.D – T.D)

(7)T.D = (B.G * 100)/(Rate * Time) 

                                                   

Simple Problems

 

1.If the true discount on a certain sum due 6 months hence at

15% is Rs 120.What is the bankers discount on the same for same

time and the same rate.

 

Sol:-            B.G = S.I on T.D

                     = RS (120 * 15 * ½  * 1/100)

                     = 9

     (B.D) – (T.D) = 9

                B.D = 120 + 9 =129

 

2.The bankers discount on Rs 1800 at 12 % per annum is equal to the

true discount on Rs 1872 for the same time at the same rate .Find 

the time.

 

Sol:-                S.I on Rs 1800 = T.D on Rs 1872

                           P.W of Rs 1872 is Rs 1800

                          Rs 72 is S.I on Rs 1800 at 12%

                           Time = (100 * 72)/(12 * 1800)

                                    = 1/3 years = 4 months

 

3.The bankers discount and true discount on a sum of money due 8 months

    hence are Rs.120 & Rs.110 resp. Find the sum  & the rate per cent

 

Sol:-                      Sum = (B.D * T.D) / (B.D) – (T.D)

                                      = (120 * 110) / (120 – 110)

                                      = 1320

      Since B.D is S.I on sum due, so S.I on Rs 1320 for 8 months is 

         Rs 120

                            Rate = (100 * 120) / (1320 * 2/3)

                                     = 13  7/11%

Medium Problems

 

1.The Bankers discount on Rs 1650 due a certain time hence is Rs 165.

find the true discount and the bankers gain.

 

Sol :-                 Sum = (B.D * T.D) / (B.D – T.D)

                                  = (B.D * T.D) / B.G

                    T.D/B.G = Sum/B.D =650/165 =10/1

                 Thus if B.G is Rs 1 ,T.D = Rs 10

                       if B.D is Rs 11 ,T.D = Rs 10

                       if B.D is Rs 165,T.D = Rs (10/11 * 165) = 150

                             B.G =Rs(165 – 150) = Rs 15

2.The Present worth of a bill due something hence is Rs 1110 and the

true discount on the bill is Rs.110 . Find the bankes discount & the 

bankers gain.

 

Sol:-               T.D = sqrt (P.W * B.G)

                       B.G = (T.D)^2 /P.W

                           = (110 * 110) / 1110

                           = 11

                       B.D = (T.D + B.G)

                           =  (110 + 11)

                           = Rs 121

 

3.What rate percent does a man get for his money when in discounting

 

Sol:-      Let the amount of the bill =100

                      Money deducted = 10

   Money received by the holder of the bill = (100 – 10)

                                            = 90

                  S.I on Rs 90 for 10 months = 10

                              Rate = (100 * 10) / (90 * 10/12)

                                   = 13 1/3%

                                                   

Complex Problems

 

1.A bill for Rs.6000 is drawn on July 14 at 5 months . It is 

discounted on 5th October at 10%.Find the bankers discount 

true discount, bankers gain and the money that the holder of

the  bill receives.

 

Sol:-                     

Face value of the bill = Rs.6000

date on which the bill was drawn = July 14 at 5 months

                      nominally due date = December 14

                      legally due date = December 17

          Date on which the bill was discounted = October 5     

       Unexpired time : Oct     Nov     Dec

                        26 +  30   +   17   =  73days =1/5 years

                    B.D = S.I on Rs 6000 for 1/5 year

                           = Rs (6000 * 10 * 1/5 * 1/100) = Rs 120

                    T.D = Rs(6000 * 10 *1/5)/(100 + (10 * 1/5))

                        = Rs. 117.64

                     B.G = (B.D) – (T.D)

                         = Rs(120 -117.64)

                         = Rs 2.36

           Money received by the holder of the bill

                         = Rs(6000 – 120) = 5880

 

                                      

2. The bankers gain on a certain sum due  1 ½ year hence 

is 3/25 of the bankers discount .The rate percent is

 

Sol:-        Let B.D = 1 then B.G = 3/25         

                    T.D = (B.D – B.G)

                       = (1 – 3/25)

                       = 22/25

           sum = (1 * 22/25) / (1 – 22/25)

               = 22/3

           S.I on Rs 22/3 for 1 ½ year is 1.

                        Rate = (100 * 1) / (22/3 * 3/2)

                            = 9 1/9%

 

3. The bankers gain of a certain sum due 2 years hence 

at 10% per annum is Rs 24 .The percent worth is

 

Sol:-          

                         T.D = (B.G * 100) / (Rate * Time)

                           00) / (10 * 2)

                             = 120.

                        P.W = (100 *T.D) / (Rate * Time)

                            = (100 * 120) /(10 * 2)

                            = 600