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

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 these types 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 amount in each year) in nominal terms to exactly pay for the vacation home if your investments earn 4% APR (compounded annually) in nominal terms?

Expert Solution

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

jeff jeffy answered 3 months ago

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