$\text { Suppose you buy an inflation-indexed bond that will adjust with inflation and thus pay you } \$ 1,500 \text { in real (inflation- }$ adjusted) terms each year for the next five years, plus your real principal of $75,000 at the end of the fifth year.The nominal interest rate is 5 percent and the expected inflation rate is 2 percent.What is the present value of the bond? (Round off your answer to the nearest thousand dollars and pick the answer closest to the one you calculate.)
A)$65,000
B)$68,000
C)$72,000
D)$75,000

Question

Quizplus · Accepted Answer

We can use the formula for present value of an annuity: PV = PMT x ((1 - (1/(1+r)^n))/r) + FV/(1+r)^n, where PV is the present value, PMT is the annual payment, r is the nominal interest rate, n is the number of years, and FV is the future value. Plugging in the values, we get PV = $14,395 x ((1 - (1/1.05^5))/0.05) + $75,000/1.05^5 = $72,181. Rounded to the nearest thousand dollars, the answer is $72,000, which is closest to choice C.