P5–46 Inflation, time value, and annual deposits While vacationing in Florida, John Kelley saw the vacation home of his dreams. It was listed with a sale price of

$200,000. The only catch is that John is 40 years old and plans to continue working until he is 65. Still, he believes that prices generally increase at the overall rate of inflation. John believes that he can earn 9% annually after taxes on his investments.

He is willing to invest a fixed amount at the end of each of the next 25 years to fund the cash purchase of such a house (one that can be purchased today for $200,000) when he retires.

a. Inflation is expected to average 5% per year for the next 25 years. What will John’s dream house cost when he retires?

b. How much must John invest at the end of each of the next 25 years to have the cash purchase price of the house when he retires?

c. If John invests at the beginning instead of at the end of each of the next 25 years, how much must he invest each year?