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