Shortcut tricks of True discount and Banker's Discount

Tricks

1. If rate of interest is R% per annum, time is T yr and present worth is PW, then true discount (TD)
                            = PW × R × T / 100

2. If rate of interest is R% and money due (for amount) is A after T yr. then
           Present Worth (PW) =  100 × A / ( 100 + R × T)

3. If money due A, rate of interest R% and time T are given, then true discount (TD) = A × T × R / ( 100 + R × T)

4.If the face value A, remaining time T and rate R% are given, then Banker's Discount (BD) = A × R × T / 100

5. If the face value of a bill due T yr hence is A and rate is R%, then Banker's Gain (BG) = TD × TD /PW

6. If the true discount at a bill due T yr hence is TD and annual rate of interest is R%, then Banker's Gain (BG)
                     = TD × R × T / 100

7. If the face value on a bill is A and true discount is TD
       then BD = A × TD / (A - TD)
Q. What will be the true discount for the present worth of  6000 for a period of 9 months at 12% per annum?

Solution Given that T = 9 month = 9 / 12 yr
                                    R = 12%, PW = 6000
Therefore TD = PW × R × T / 100
                         = 6000 × 12 × (9/12) / 100
                         = 60 × 9 = 540

Q. Find the present worth of  1860 due 3 yr hence at 8% per annum. Also, find the true discount.

Solution Given that A = 1860, R = 8%, T =3 yr
According to the formula,
           PW =    100 × A / ( 100 + R × T)
                   = 100 × 1860 / ( 100 + 8 × 3)
                   = 100 × 1860 / 124
                   = 1500
           TD = A - PW
                 = 1860 - 1500
                 = 360

Q. Find the sum due, if the true discount on a sum due 2 yr hence at 14% rate of interest be  336.

Solution Given that T = 2 yr, R = 14%, TD = 336
        Sum due(A) =?
According to the formula,
   true discount (TD) = A × T × R / ( 100 + R × T)
                              336 = A × 2 × 14 /( 100 + 14 × 2) = 28A / 12      Therefore               A = 1536

Q. Find the banker's discount at a bill of  25500 due 2 months hence, when rate of interest is 3% per annum.

Solution Given that A = 25500, R = 3%,
    T = 2 months = 2/12 = 1/6 yr, BD =?
According to the formula,
                   (BD) = A × R × T / 100
                            = 25500 × 3 × (1/6)/100
                            = 127.5

Q.The true discount at a bill of  3720 due 8 months hence is 120. Find the banker's gain.

Solution
Present Worth of bill = 3720 - 120 = 3600
  Therefore Banker's Gain (BG) = TD × TD /PW
                                         = 120 × 120 / 3600
                                         = 144 / 36 = 4

Q. If the banker's gain is 180 at a bill due 6 yr hence at 10% per annum, find the banker's discount.

Solution Given that BG = 180, R = 10%, T = 6yr
According to the formula,
                 BG = TD × R × T / 100
                180 = TD × 10 × 6 / 100
                 TD = 300
As we know that BG = BD - TD
                                BD = BG + TD = 180 + 300 = 480

Q.The true discount on a bill of 900 is 100. Find the banker's discount.

Solution Given
                A = 900,  TD = 100
According to the formula
               BD = A × TD / (A - TD)
                     = 900 × 100 / (900 - 100)
                     = 112.5

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