FeedBack Form

Your Name :
Your Email :
Your Location :
Your Message :
   
FeedBack

Bankers Discount

Aptitude

BANKERS DISCOUNT -> IMPORTANT CONCEPTS

Bankers’ Discount : Suppose a merchant A buys googds worth, say Rs. 10,000 from another merchant B at a credit of say 5 months. Then, B prepares a bill, called the bill of exchange. A signs this bill and 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. Three days (known as grace days) are added to it to get a date, known as legally due date.

Suppose B wants to have the money before the legally due date. Then he can have the money from the banker or a broker, who deducts S.I. on the face value (i.e., Rs. 10,000 in this case) for the period from the date on which the bill was discounted (i.e., paid by the banker) and the legally due date. This amount is known as Banker’s Dicount (B.D.)

Thus, B.D. is the S.I. on the face value for the period from the date on which the bill was discounted and the legally due date.

Banker’s 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.

BANKERS DISCOUNT -> IMPORTANT FORMULAE

I. B.D. = S.I. on bill for unexpired time.
II. B.G. = (B.D.) - (T.D.) = S.I. on T.D. = (T.D.)² / R.W.
III. T.D. = √P.W. * B.G.
IV. B.D. = [Amount * Rate * Time / 100]
V. T.D. = [Amount * Rate * Time / 100 + (Rate * Time)]
VI. Amount = [B.D. * T.D. / B.D. - T.D.]
VII. T.D. = [B.G. * 100 / Rate * Time]

BANKER’S DISCOUNT -> SOLVED EXAMPLES

1. What rate percent does a man get for his money when is discounting a bill due 10 months hence, he deducts 10% of the amount of the bill
  Sol.Let, amount of the bill = Rs. 100. Money deducted = Rs.10.
Money received by the holder of the bill = Rs. (100 - 10) = Rs. 90.
∴ S.I. on Rs. 90 for 10 months = Rs. 10.
∴ Rate = [100 * 10 / (90 * 10/12)] % = 13⅓%.
2. The banker’s gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker’s discount is:
  T.D. = [B.G. * 100 / R * T] = Rs. [270 * 100 / 12 * 3] = Rs. 750.
3. The banker’s discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the sum and the rate percent.
  Sol.
Sum = [B.D. * T.D. / B.D. - T.D.] = Rs. [120 * 110 / 120 - 110] = Rs. 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%

BOATS AND STREAMS -> EXERCISE

6. The banker’s gain on a certain sum due 1½ years hence is 3/25 of the banker’s discount. The rate percent is :
 
  • A. 3 1/3 %
  • B. 6 1/6 %
  • C. 9 1/9 %
  • D. 9 1/6 %
Ans: C.
Sol.
Let B.D. = Re 1. Then, B.G. = Re 3/25.
∴ T.D. = (B.D. - B.G.) = Re[1 - 3/25] = Re 22/25.
Sum = [1 * 22/25 / 1 - 22/25] = Rs. 22/3.
S.I. on Rs. 22/3 for 1 ½ years is Re 1.
∴ Rate = [100 * 1 / 22/3 * 3/2] % = 9 9/1%.
 
7. The present worth of a certain bill due sometime hence is Rs. 800 and the true discount is Rs. 36. The banker’s discount is :
 
  • A. Rs. 37.62
  • B. Rs. 38.75
  • C. Rs. 39.40
  • D. Rs. 39.96
Ans: A.
Sol.
B.G. = (T.D.)² / P.W. = Rs. [36 * 36 / 800] = Rs. 1.62.
∴ B.D. = (T.D. + B.G.) = Rs. (36 + 1.62) = Rs. 37.62.
 
8. The Banker’s gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:
 
  • A. 30
  • B. 40
  • C. 50
  • D. 60
Ans: C.
Sol.
T.D. = B.G. * 100 / R * T = Rs.[6 * 100 / 12 * 1] = Rs.50
 
9. The present worth of a certain sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. Then banker’s gain is:
 
  • A. 16
  • B. 18
  • C. 20
  • D. 21
Ans: A.
Sol.
B.G. = (T.D.)² / P.W. = Rs.[160 * 160 / 1600] = Rs. 16.
 
10. The banker’s gain on a sum due 3 years hence at 12% per annum is Rs. 270. Then banker’s discount is :
 
  • A. 500
  • B. 750
  • C. 890
  • D. 1020
Ans: D.
Sol.
T.D. = [B.G. * 100 / R * T] = Rs.[270 * 100 / 12 * 3] = Rs.750.
∴ B.D. = Rs. (750 + 270) = Rs.1020.