Question 172901: Joe wants to buy a house but does not want to get a loan. The average price of the dream house is $500,000 and its price is growing at 5 percent per year. How much should Joe invest in a project at the end of each year for the next 5 years in order to accumulate enough money to buy his dream house with cash at the end of the fifth year? Assume the project pays 12 percent rate of return.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! value of the house today is 500,000
in 5 years, the house will appreciate 5 years worth of interest which makes the formula for the future value of the house:
500,000 * (1.05)^5 = 638140.78
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if he invests in a project at the end of each year and the project earns 12% a year, then he would have to invest 100449.57 each year to equal 638140.78 at the end of the 5th year.
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this is how it works out:
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at the end of the first year he invests: $100,449.57
at the end of the second year this is multiplied by 1.12 to equal: $112,503.52
he invests an additional $100,449.57 to make this equal: $212,953.09
at the end of the third year this is multiplied by 1.12 to equal: $238,507.46
he invests an additional $100,449.57 to make this equal: $338,957.03
at the end of the fourth year this is multiplied by 1.12 to equal: $379,631.87
he invests an additional $100,449.57 to make this equal: $480,081.44
at the end of the fifth year this is multiplied by 1.12 to equal: $537,691.22
he invests an additional $100,449.57 to make this equal: $638,140.79
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he has invested 100,449.57 at the end of each year and this has accumulated and grown to equal $638,140.79 by the end of the fifth year.
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the value of the house has grown 5% per year for 5 years to equal $638,140.79.
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he has invested just enough money to buy the house with cash assuming no taxes have to be paid on the investment.
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there is a formula to derive this.
that formula has to do with the annuity from a future amount.
i used a calculator to get the answer.
if you had to use the formula, the formula would be:
which is the same as:
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FV is the future value which is the same as future amount.
i is the periodic interest rate which is annual in this case.
n is the number of time periods which is years in this case.
PMT is the annual payment.
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this formula is for a payment at the end of a period which was what your problem was asking about.
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i checked the formula out and it works.
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