Inflation, time value, and annual deposits Personal Finance ProblemWhile vacatio
ID: 2774879 • Letter: I
Question
Inflation, time value, and annual deposits Personal Finance ProblemWhile vacationing in Florida, John Kelley saw the vacation home of his dreams. It was listed with a sale price of $239,000. The only catch is that John is 35 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 8% annually after taxes on his investments. He is willing to invest a fixed amount at the end of each of the next 30 years to fund the cash purchase of such a house (one that can be purchased today for $239,000) when he retires. a. Inflation is expected to average 3% a year for the next 30 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 30 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 30 years, how much must he invest each year?Explanation / Answer
a)
John is going to retire after 30 years
Cost of Dream house after 30 years = $239,000 * (1+0.03)30 = $239,000 * 2.427 = $580,053
b)
Future Value = Annual Invetsment * {[(1+ r)t - 1 ]/r}
$580,053 = Annual Investment * {(1.0830-1)-1/.08} = Annual Invetsment * 113.283
Annual Investment = $580,053 / 113.283 = $5120.39
c)
If john plans to invets in the beginning of each year then, he will have one additional year to eran interest ans therefore his annual investment will be smaller.
The value of house at the beginning of year 65 = Value of house at the end of year 65 / 1.08
= $580,053 / 1.08 = $537,086
John have to invest annually to get this amount at the beginning of year 65. This amount will earn 8% interest to be provide the cost of house at the end of year 65.
Annual investment = $537,086 / 113.283 = $4,741.10