# Banker's Discount Questions

FACTS  AND  FORMULAE  FOR  BANKER'S  DISCOUNT  QUESTIONS

Banker's Discount :

Suppose a merchant 'A' buys goods 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 Discount (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.

IMPORTANT FORMULAE

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

2. B.G = (B.D) - (T.D) = S.I  on $T.D=\frac{{\left(T.D\right)}^{2}}{P.W}$

3. $T.D=\sqrt{P.W×B.G}$

4. $B.D=\left(\frac{Amount×Rate×Time}{100}\right)$

5. $T.D=\left[\frac{Amount×Rate×Time}{100+\left(Rate×Time\right)}\right]$

6. $Amount=\frac{B.D×T.D}{B.D-T.D}$

7. $T.D=\frac{B.G×100}{Rate×Time}$

Q:

The B.G. on a certain sum 4 years hence at 5% is Rs. 200. What is the present worth?

 A) Rs. 4500 B) Rs. 6000 C) Rs. 5000 D) Rs. 4000

Explanation:

T = 4 years

R = 5%

Banker's Gain, BG = Rs.200

$TD=PW×BG$

$⇒1000=PW×200$

=>PW = Rs.5000

3 2148
Q:

The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker's discount and the banker's gain.

 A) Rs.145 B) Rs.136 C) Rs.121 D) Rs.112

Explanation:

T.D. =Ö(P.W.*B.G)

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

= Rs.[(110x110)/ 1100]

= Rs. 11.

B.D.= (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.

1 2093
Q:

The true discount on a bill of Rs. 2160 is Rs. 360. What is the banker's discount?

 A) Rs. 432 B) Rs. 422 C) Rs. 412 D) Rs. 442

Explanation:

F = Rs. 2160

TD = Rs. 360

PW = F - TD = 2160 - 360 = Rs. 1800

True Discount is the Simple Interest on the present value for unexpired time

=>Simple Interest on Rs. 1800 for unexpired time = Rs. 360

Banker's Discount is the Simple Interest on the face value of the bill for unexpired time

= Simple Interest on Rs. 2160 for unexpired time

=(360/1800)* 2160

= (1/5) * 2160

=Rs. 432

0 2043
Q:

The bankers discount and true discount on a sum of money due 8 months hence are Rs.120 & Rs.110 resp. Find the sum.

 A) 1457 B) 1320 C) 1140 D) 1260

Explanation:

Sum = (B.D * T.D) / (B.D) -(T.D)

= (120 * 110) / (120 -110)

= 1320

2 1960
Q:

The present worth of a certain sum due sometime hence is Rs. 3400 and the true discount is Rs. 340. The banker's gain is:

 A) Rs. 21 B) Rs. 17 C) Rs. 18 D) Rs. 34

Explanation:

$BG=TD2PW=(340)23400=Rs.34$

0 1631
Q:

What is the present worth of a bill of Rs.1764 due 2 years hence at 5% compound interest is

 A) Rs. 1600 B) Rs. 1200 C) Rs. 1800 D) Rs. 1400

Explanation:

Since the compound interest is taken here,

$PW1+51002=1764$

=> PW = 1600

0 1608
Q:

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.

 A) Rs.109 B) Rs.119 C) Rs.129 D) Rs.139

Explanation:

B.G = S.I On T.D

= Rs. (120 * 15 * 1/2 * 1/100)

= Rs.9

B.D - T.D = Rs.9

B.D = Rs.(120 +9) = Rs.129

1 1563
Q:

The B.D. and T.D. on a certain sum is Rs.200 and Rs.100 respectively. Find out the sum.

 A) Rs. 400 B) Rs. 300 C) Rs. 100 D) Rs. 200

$F=BD×TDBD-TD=200×100200-100=200×100100=Rs.200$