The present value of a perpetuity is equal to the payment on the annuity, PMT, divided by the interest rate, I: PV − PMT/I. What is the future value of a perpetuity of PMT dollars per year? (Hint: The answer is infinity, but explain why.)

If the present value of a perpetuity is equal to payment divided by interest rate (PMT/I), then the future value of the perpetuity is equal to present value of perpetuity multiplied by (1 + I)' 't'. 

Equation format: 

Present value of perpetuity PMT 

PV = I 

then 

FY = PMT x (1 + I)oo I 

Next, we know that (1 + I)n gets larger as n increases. So if n = infinity, then (1 + I)O° = infinity. 

Thus: 

PMT FY = I x (1 + 1)OD = infinity.