What is the reasoning for the Discount Factor formula? I've previously come across dicount factors in my high school education but we had formula sheets so I never bothered actually learning it. In my university I have a business class in which we are now going over dicounted cash flows. Now that I'm a much more enthusiatic learner I would really like to know why the discount formula works and/or the reasoning behind it. The formula is as follows:
Discount factor = 1 / (1 + r)^t

where r is the discount rate and t is the amount of years.
This is more business related than math related. So if your wondering why I posted this here I figured that mathmaticians would be able to better explain the reason/origins of the formula, whereas all I've gotten from asking business realted experts is pretty much 'the fomula works so it's good enough for me' sort of answers.

This is annually compounded interest ($r$ is the interest rate) run backwards in time (going back $t$ years).
If you start with $P_0$ dollars and are using interest compounded annually, then after 1 year $P_0$ has grown to $P_1=P_0+P_0r=P_0(1+r)$ dollars [$P_0$ earns $r$ percent interest so we get $P_0r$ dollars in interest]. To see what happens after 2 years, remember that with compounded interest you must "restart" the computation every year. So at the end of year 2, you'll have $P_2=P_1+P_1r=P_1(1+r)=P_0(1+r)(1+r)=P_0(1+r)^2$ dollars.
Now we can see a pattern emerging and find that after $t$ years our original $P_0$ dollars has grown to $F=P_0(1+r)^t$ dollars. 
Given a future value $F$, we can solve to find the present value $P_0$ and get $P_0=F/(1+r)^t$. Thus the discount factor appears!
http://en.wikipedia.org/wiki/Compound_interest
