## Aptitude True Discount and Banker's Discount Concepts and Formulas## Points to Remember:
## Concept:Suppose a merchant A buys goods worth of face value Rs. 2000 (interest of one year included) from another merchant B at a credit of say 12 months or one year. The B prepares a bill called the bill of exchange, which is also known as Hundi. The merchant A signs this bill that allows B to withdraw the amount from his bank account after the specified duration of 12 months. Let the market interest rate is 5%. The date exactly after the 12 months is called the Suppose after 6 months, B needs money immediately and cannot wait till due date. In this case, B can approach a bank or broker to pay him money against the bill. In this situation, the money paid by the banker will be less than the face value of the bill. Let the bill is presented to the banker after six months, the banker will deduct the interest on the face value for the remaining period of six months and this interest is called the The interest on the bill value (face value) is called the banker's discount and the difference between the banker's discount and true discount (T.D) is called Banker's gain = Banker's discount - True discount B.G. = Interest on the sum due for the unexpired time - Interest no present worth for the unexpired time = Interest on (sum due - present worth) So, true discount = Face value - Present value = 2000 - 1951.23 = 48.77 The In other words, the So, if the bank pays Rs. 1951.23 (present worth) to B in exchange for the bill, the bank would not make a profit from this deal. So, the bank does not use true discount but uses another formula to calculate the discount called Banker's Discount.
Banker's Discount = FV * r * t = 2000 * 0.05 * (½) = 50 So, instead of discounting true discount, the Banker discounts the banker's discount from the face value and pays out Rs. 2000 - 50 = Rs.1950 So, B.G. = Banker's discount - True Discount = 1.23
Let the rate of interest = R% per annum Banker's Discount (B.D) = S.I (simple interest) on bill for unexpired time
Suppose a merchant has to pay Rs. 164 after 4 years and the rate of interest is 16% per annum. It shows Rs. 100 will amount to Rs. 164 in 4 years. So, a payment of Rs. 164 will clear off the debt of Rs. 164 due 4 years hence. AS per the above example: We define: T.D. = Interest on P.W so, the Amount Due = P.W + T.D. ## Note: If the date of the bill is not given, grace days are not required to be added.Aptitude True Discount and Banker's Discount Test Paper 1 Aptitude True Discount and Banker's Discount Test Paper 2 Aptitude True Discount and Banker's Discount Test Paper 3 |

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