You may have learned the concepts of Bills of Exchange and Commercial papers in accountancy. However, after the conceptual learning comes to the practical applications of these bills. One such aspect is the discounting of bills. Here we will learn what is discounted bill and how such discount is calculated with the help of some formulas. Let us get started.

## What is Discounted Bill

First, let us get a clear idea of what is meant by discounting of bills. Bill discounting is the fee or the ‘discount’ that a bank charges a seller of the bill in exchange of releasing the funds to him before the due date of the bill. Essentially, bill discounting is the exchange of the bill for money, either from a bank or any third party.

*Present Value*

To fully understand the concept of bill discounting, we need to learn about a few more important terms. One of these terms is present value (PV). Present Value is the current value of a sum of money in the future. So by discounting this future sum of money by a fixed discount rate, we arrive at its present value.

Hence, the higher the discount rate, lower the present value of the sum of money. It is an inverse proportion. Present Value indicates that an ‘x’ amount of money is worth more in the present than the same amount is in the future.

Present Value (PV) = \( \frac{Future Value}{(1+r)^n} \)

- r = rate of return
- n= number of years/periods

*True Discount*

This is also an important concept to learn in the discounting of bills. Now the total sum of money due at the end is known as the “Amount (A)”. The present worth or value of this sum is the PV.

The difference between the two is what we call the “True Discount (TD)”. Basically, the interest accrued on the Present Value of the sum is the True Discount. Let us learn its formula.

TD = Amount/Future Value – Present Value

TD = FV – \( \frac{Future Value}{(1+r)^n} \)

Now while True Discount is the interest amount on the Present Value, there is another term known as the Bankers Discount. This is actually the Simple Interest on the face value of the sum from the date of the discounting to the due date of the bill.

Hence, the difference between the true discount and the bankers discount (fee for discounting the bill early) is known as the Bankers Gain.

## Solved Examples on Discounting of Bills

Q: The amount due on a bill is after its maturity in 6 months is 1040. The rate of interest is 8%. Find the True Discount.

Ans: alculation will be as follows,

TD = Amount/Future Value – Present Value

TD = \( \frac{A*n*i}{1+ni} \)

Therefore,

TD = \( \frac{1040*0.5*0.08}{1+0.04} \)

TD = 40

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