Inflation, time value, and annual deposits Personal Finance Problem. While vacationing in Florida, John Kelley saw the vacation home of his dreams. It was listed with a sale price of $$153,000.$ The only catch is that John is $42$ years old and plans to continue working until he is $65.$ John believes that prices generally increase at the overall rate of inflation and that he can earn $8\%$ on his investments. He is willing to invest a fixed amount at the end of each of the next $23$ years to fund the cash purchase of such a house $($one that can be purchased today for $$153,000)$ when he retires.

a$.$ Inflation is expected to average $4\%$ a year for the next $23$ 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 $23$ 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 $23$ years, how much must he invest each year?

a$.$ When he retires, John's dream house will cost $ $($Round to the nearest cent.$)$