Present Value of a Perpetuity A perpetuity pays $100 per year and interest rates are 6.5 percent.How much would its value change if interest rates increased to 9 percent?

Question

Quizplus · Accepted Answer

The formula for the present value of a perpetuity is PV = PMT / r, where PV is the present value, PMT is the payment per period, and r is the interest rate per period. In this case, PMT = $100 and r = 6.5% = 0.065, so PV = $100 / 0.065 = $1,538.46.

If the interest rate increases to 9% = 0.09, the new present value would be PV' = $100 / 0.09 = $1,111.11. The change in value is the difference between the old and new values, so PV' - PV = $1,111.11 - $1,538.46 = -$427.35. Therefore, the value would decrease by $427.35. The answer is D, $427.35 decrease.

Present Value of a Perpetuity a Perpetuity Pays $100 Per