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You would like to purchase a vacation home in 15 years. The current price of such...

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Finance

You would like to purchase a vacation home in 15 years.
The current price of such a home is $275,000 but the price of thesetypes of homes is rising at a rate of 3% per year.
How much would you have to invest in years 1 to 5, (the same amountin each year) in nominal terms to exactly pay for the vacation homeif your investments earn 4% APR (compounded annually) in nominalterms?

Answer & Explanation Solved by verified expert
4.5 Ratings (966 Votes)

Vacation home purchase horizon in years 15
Current price $                            275,000
Annual price increase 3.00%
Price after 15 years Current price * (1+rate)^time
Price after 15 years 275000 * (1+3%)^15
Price after 15 years                           428,441.04
Future value of annual deposit from year 1 to 5 at T15 should be equal to 428,441.04
Annual return 4%
Calculation of future value factors
Year FV factor at t15= (1+rate)^(15-deposit year)
1 1.73168
2 1.66507
3 1.60103
4 1.53945
5 1.48024
Total 8.01748
Assumed annual deposit P
P*8.01748=                           428,441.04
P= =428441.039/8.01748
P=                             53,438.37
So annual deposit should be 53,438.37
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