How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume an interest rate of 10% and cash flows at the end of each period.

The perpetuity is worth $1486.43 more than the ordinary annuity

Explanation:

A perpetuity that with an annual cash inflow or cash outflow payable for a foreseeable future - for an infinite number of period

The present value of a perpetual annuity is calculated as

PV= A/r

PV = 1000/0.1

PV =&10,000

On the other hand, an annuity with  annual cash inflows or cash outflows for certain number of years is called an ordinary annuity.

The present value of an ordinary annuity is determined as follows:

PV = (1 - (1+r)^n)/r   × A

     = (1-(1+0.1)^(-20))/0.1 × 1000

    = 8.5135  × 1000

   = 8513.56

Difference in PV =  10,000 - 8513.56

                            = $1486.43

The perpetuity is worth $ 1,486.43 more than the ordinary annuity

$1,486.44

Explanation:

The additional value that the perpetuity will generate will be the difference between the perpetuity present value and annuity present value.

So here

PV of the Perpetuity = Cashflow / r

PV of the Perpetuity = $1,000/.10 = $10,000

PV of the Annuity = Annual Cash flow * Annuity factor at 20 years

PV of the Annuity = $1,000 * [1 - (1/1.10)^20] / 0.10

PV of the Annuity = $8,513.56

Difference between perpetuity and annuity = $10,000 - 8,513.56 = $1,486.44