Discount Factor

The discount factor $v$ is the Present Value of $1$ payable one period in the future:

$v = \frac{1}{1+i}$

$= 1 - d$

$i$ is the effective Interest Rate and $d$ is the Discount Rate.
The $n$ -period discount factor is $v^n = (1+i)^{-n}$ .
The discount factor converts a future cash flow to its present value:

$\text{PV} = C \cdot v^n$

$= \frac{C}{(1+i)^n}$

Under Force of Interest $\delta$ , the discount factor is $v = e^{-\delta}$ per period.

Present Value Using Discount Factor Find the present value of $10{,}000$ due in 5 years at an effective annual rate of 4%.

Answer $v^5 = (1.04)^{-5} = 0.82193$ $\text{PV} = 10{,}000 \times 0.82193 = 8219.27$