Table of contents  
Introduction  
Important Formulas  
Solved Examples  
Tips and Tricks 
Remark: When the date of the bill is not given, grace days are not to be added.
Question 1. The true discount on a bill Rs.1860 due after 8 months is Rs.60. Find the rate, the banker’s discount and the banker’s gain.
Amount = Rs.1860, T.D. = Rs.60
∴ P.W. = Rs.(186060) = Rs. 1800
S.I. on Rs. 1800 for 8 months = Rs.60
B.D. = (T.D.) + (B.G.) = Rs. (60+2) = Rs. 62
Question 2. 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 extra gain the banker would make in the transaction.
∴ B.D. = B.G. + T.D. = Rs. (11+110) = Rs. 121
Question 3. The banker’s discount and the true discount on a sum of money due 8 months hence are Rs. 52 and Rs. 50, respectively. Find the sum and the rate per cent.
∴ B.D. is S.I. on sum due.
⇒ S.I. on Rs. 1300 for 8 months is Rs. 52
Thus,
Question 4. The banker’s discount on Rs. 1800 at 5% is equal to the true discount on Rs. 1830 for the same time and at the same rate, Find the time.
S.I. on Rs. 1800 = T.D.on Rs. 1830
∴ P.W. of Rs. 1830 is Rs. 1800
i.e., Rs. 30 is S.I. on Rs. 1800 at 5%
∴ Time = (100 × 30)/(1800 × 5) = 1/3 years = 4 months
Question 5. If the true discount on a certain sum due 6 months hence at 6% is Rs. 36, what is the banker’s discount on the same sum for the same time and at the same rate ?
B.G.= S.I. on T.D.= Rs.(3600×6×0.5)/100 = Rs.1.08
∴ (B.D.) – (T.D.) = Rs. 1.08
i.e. B.D.=(T.D.)+Rs.1.08 = Rs.(36+1.08) = Rs.37.08
Scenario: Suppose A has borrowed Rs 1000 from B and this amount should be returned with interest after 1 year. Let us assume that the market interest rate is 5% per year [Simple Interest]. A hands over to B a note with a Face Value of Rs 1050, promising repayment after 1 year. [1000 + (1000 x 0.05 x 1yr) = 1050]
After 6 months, B decides that he needs the money immediately and cannot wait till the due date which is 6 months away. B approaches a bank and hands over the note from A with Face Value of Rs 1050 due after 6 months.
Calculating True Discount:
The present value (or true value) of the note from A is calculated as follows:
PV x (1 + r x t) = FV [Here, PV is the present value, r is the rate of simple interest, t is time and FV is the Face Value of the note.]
Present Value (or True Value) = 1050/(1.025) = Rs. 1024.4
True discount = Face Value – Present Value = 1050 – 1024.4 = Rs. 25.6
But, if the bank paid out Rs 1024.4 to B in exchange for the note, the bank would not make a profit. The bank does not use True Discount but uses another formula to calculate the discount called Banker’s Discount.
Calculating Banker’s Discount:
Banker’s Discount: The Simple Interest on the Face Value of the debt for the time period between the legally due date and the date on which the bill is discounted is called Banker’s Discount.
Banker’s Discount = FV x r x t = 1050 x 0.05 x (1/2) = Rs 26.25
Note:
True Discount = FV – [FV / (1 + r x t)] = FV [r x t / (1 + r x t)] < FV x r x t
⇒ True Discount < Banker’s Discount
Instead of discounting True Discount, the Bank discounts the Banker’s Discount from the Face Value and pays out Rs 1050 – 26.25 = Rs. 1023.75
Banker’s Gain = Present Value of the Note – Actual Payout
= (Face Value – True Discount) – (Face Value – Banker’s Discount)
= Banker’s Discount – True Discount [This figure is always positive]
Example 1: The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. What is the banker’s discount?
Sol:
Banker’s Discount = FV x r x t = 0.36 x FV
True Discount = FV – PV = FV – FV / [1 + (r x t)] = FV – FV / 1.36
= 0.36 x FV / 1.36 = Banker’s Discount / 1.36
Banker’s Gain = Banker’s Discount – True Discount = BD  BD/1.36 = 270
⇒ Banker’s Discount, BD = 270 x 1.36 / 0.36 = Rs. 1020
Moving on, we come to the formulae in Banker’s Discounts.
Example 2: The banker's discount on a certain sum due 2 years hence is 11/10 of the true discount. What is the rate?
Sol:
BD = FV x r x t
TD = FV – PV = FV – FV / [1 + (r x t)] = FV x r x t / [1 + (r x t)]
BD/ TD = 1 + (r x t) = 11/10
2r = 1/10
⇒ r = 1/20 = 0.05 or 5%
Example 1: A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then what is his gain?
Sol:
Present Value = 3600/[1+(0.10 x 2)] = Rs 3000
Gain = Present Value – Cost = 0
Example 2: A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 12% per annum, how much cash should he pay?
Sol:
Face Value = Rs. 10028, r = 12% p.a.
Present Value after 9 months = 10028/[1+(0.12*9/12)] = Rs 9200
314 videos170 docs185 tests

1. What is Banker's Discount and how is it different from simple interest? 
2. How is Banker's Discount calculated? 
3. What is the formula to find the Banker's Gain in a transaction involving Banker's Discount? 
4. How is Banker's Discount used in reallife scenarios? 
5. Can Banker's Discount be negative? 
314 videos170 docs185 tests


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