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9-7 The present value of a perpetuity is equal to the payment on the annuity, PMT,...

9-7 The present value of a perpetuity is equal to the payment on the annuity, PMT, divided by the interest rate, r: PVP PMT r. What is the sum, or future value, of a perpetuity of PMT dollars per year? (Hint: The answer is infinity, but explain why.)

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Answer #1

The future value of cash flow, PMT is given by

FV of cash flows= PV * [(1+ r)^n]

We know , PV =( PMT / r) , as per the formula for Perpetuity

So FV of Perpetuity = (PMT/r) *[(1+r)^n]

For a perpetuity n is number of years tends to infinity ()

As N , T ,

The entire RHS(Right hand side)

Hence, FV of Perpetuity

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