Present Value of a Perpetuity

Question 1

What is a perpetuity?

Answer 1

An ordinary annuity that extends indefinitely.

Question 2

What is the formula to calculate PV of an ordinary perpetuity? (the easy one)

Answer 2

PV=A/r

Question 3

How do you calculate the PV of a Projected Perpetuity at t=0?

Answer 3

PV=A/r + one period of time before that.

Question 4

How do you calculate the PV of an Ordinary Annuity as the PV of a Current Minus Projected Perpetuity?

Answer 4

First we find PV1 (ordinary annuity):
PV=A/r,
then PV2(t-projected perpetuity)=PV1(1+r)^N