You are willing to pay $15,625 to purchase a perpetuity which will pay you and your heirs $1,250 each year,forever.If your required rate of return does not change,how much would you be willing to pay if this were a 20-year,annual payment,ordinary annuity instead of a perpetuity?

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Quizplus · Accepted Answer

The present value of a perpetuity is calculated as the annual payment divided by the required rate of return. Here, $15,625 = $1,250 / r, so r = 0.08 or 8%. For a 20-year ordinary annuity, the present value is calculated using the formula for the present value of an annuity: PV = PMT * [(1 - (1 + r)^-n) / r]. Substituting the values: PV = $1,250 * [(1 - (1 + 0.08)^-20) / 0.08] = $12,273.

You Are Willing to Pay $15,625 to Purchase a Perpetuity