## Best explanation to understand and solve the true discount problems.

This section contains the aptitude questions based on TRUE DISCOUNT.

Here, you have the explanation for true discount, some important terms of true discount and also the important formulas of true discount.

Learn the given explanation and try to find the solution for the aptitude questions in our website which will be a practice for you to attend any entrance or competitive exams.

### What is meant by true discount?

True discount is the difference between the present worth of the money and the actual amount.

It can also be said as the interest in any present worth for the amount of time, the debt is due to be discharged.

What is the concept of true discount?

Consider a merchant ‘A’ buys goods worth of face value Rs. 2000 (including the interest for one year) 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’ will sign this bill that allows ‘B’ to withdraw the amount from his bank account after the given period of 12 months.

What is nominal due date and legally due date?

Now, let the market interest rate is 5%. The exact date after the given period of 12 months is called the nominal due date. Also , 3 days grace period is also given to this date of expiry and this date is legally the due date.

For example: If 10th January  2010 is the nominally due date, 13 January 2010 will be legally due date.

The amount Rs. 2000 is called the face value. So, according to the bill, the ‘B’ will receive a face value of Rs. 2000 after twelve months.

But suddenly after 6 months, ‘B’ says that he needs money immediately and he cannot wait till due date. In this case, ‘B’ can approach a bank or broker to pay him money against this bill. In such a situation, the money given by the banker to ‘B’ will be less than the face value of the bill.

How is present value of bill calculated?

The present value of the bill is calculated by

PV  x (1+r x T) = FV

PV = present value

r = rate of interest

t = time

FV= face value

So, the present value or the true value is equal to 2000 / 1.025 which is equal to 1951.23

so, true discount = Face value – Present value that is 2000 – 1951.23 which is equal to  48.77

The true discount is nothing but the difference between the face value or sum due at the end of the given time and its present worth. So, in the given example,

True discount = Face value – Present value. That is 2000 – 1951.23 = 48.77

In other words, the true discount is the simple interest on the present value or worth for the unexpired time.

In other words, the present value or present worth of a sum of money due at the end of a specified time is that sum which will amount to the sum due with its interest for the given time at the given rate.

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 will not use true discount but uses another method or formula to calculate the discount which is called Banker’s Discount.