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4

Well this is 'exponential discounting'. An infinite sum of geometric series: $$\sum R+ R\delta + R\delta^2.... R\delta^t = \frac{R}{1-\delta}, \text{ if } |\delta|<1$$ Now lets call the denominator rho $1-\delta= \rho$. The exponential discounting is there since its an infinite sum of geometric series. Edit: In response to Giskard's +1 comment I tried to ...

4

You are right the two series closely follow each other for the reasons you mention. During quite some time the discount rate actually used to be a ceiling for a funds rate. This is precisely, because if the federal funds rate was below the discount rate, most banks adjusted their reserve positions in the federal funds market and when the federal funds rate ...

3

An answer (I am not sure this is the right one) is if the "positive rate $\rho$" refers to an interest rate. Sometimes interest rates are referred to as discount rates. In this case we would have a discount factor of $1/(1+ \rho)$, and the usual present value formula for a perpetual annuity yields \frac{R}{1+ \rho} + \frac{R}{(1+ \rho)^2} + \frac{...

2

To be clear, we are assuming that the nominal investment value is a constant $K$. As such, if we calculate the NPV in the future, that future NPV will rise. Of course, we do not work with future NPV’s, we are making a decision now, and so we need to discount that future NPV by the discount rate, to get an apples-to-apples comparison. I will now look at the ...

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