9.19. You need to insure your home over the next 20 years. You can either pay beginning-of-year premiums with today’s premium of $5,000 and future premiums growing at 4 percent per year, or prepay a lump sum of $67,500 for the entire 20 years of coverage.

a. With a rate of 9 percent compounded annually, which of the two choices would you prefer?

b. How would your answer change if the rate were 10 percent compounded annually?

c. What is happening to the PV of the annuity as r increases?