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Business Mathematics and Statistics · Ch 6 — Discounting of Bills of Exchange

True Discount and Present Value

4

True Discount and Present Value

The present value (PV) of a bill is the amount which, if lent out today at the given rate of simple interest, would grow to exactly the face value FF by the maturity date. In other words, it is the fair worth of the bill right now.

Since FF is the present value plus the interest it earns over time tt:

F=PV(1+rt100)⇒PV=100 F100+rtF = PV\left(1 + \dfrac{rt}{100}\right) \quad\Rightarrow\quad PV = \dfrac{100\,F}{100 + rt}

The true discount (TD) is the fair deduction — the interest on the present value (not on the face value) for the unexpired period:

TD=PV×r×t100=F×r×t100+rtTD = \dfrac{PV \times r \times t}{100} = \dfrac{F \times r \times t}{100 + rt}

and equivalently

TD=F−PV.TD = F - PV. …

Definition 1Present Value (PV)

The sum which, invested today at the given rate, would amount to the face value at maturity; $PV …

Definition 2True Discount (TD)

The simple interest on the present value for the unexpired period; the fair deduction, $TD = F,rt/( …

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