SOLUTION: Debbie plans to buy a house for cash instead of paying a mortgage. She is willing to set aside $12 OOO at the end of each year for 15 years. She invests the money in a high-risk mu

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Question 1207431: Debbie plans to buy a house for cash instead of paying a mortgage. She is willing to set aside $12 OOO at the end of each year for 15 years. She invests the money in a high-risk mutual fund, which has traditionally earned 9.2% annually. Money decreases in value by 2.5% per annum. How much will Debbie have saved after 15 years?

Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
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she is willing to set aside 12000 at the end of each year for 15 years.
she invests this at 9.2% per year for 15 years.

i think the way to solve this is to calculate it in today's dollars and then determine the value that it will be in tomorrow's dollars.

using the texas instruments business analyst 2 calculator, i get the future value of 12000 dollar payments at the end of each year for 15 years at 9.2% interest rate per year to be equal to 357,917.2439.

that's in today's dollars.

in tomorrow's dollars, at an inflation rate of 2.5% per year, that would be equal to 357,917.2439 / 1.025^15 = 247129.5291.



Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Debbie plans to buy a house for cash instead of paying a mortgage.
She is willing to set aside $12 OOO at the end of each year for 15 years.
She invests the money in a high-risk mutual fund, which has traditionally earned 9.2% annually.
Money decreases in value by 2.5% per annum. How much will Debbie have saved after 15 years?
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First, calculate the future value of the ordinary annuity

    FV = P%2A%28%281%2Br%29%5En-1%29%2Fr,


where  P is the annual payment at the end of each year (P = %12000);

       r is the rate of 9.2% (which is 0.092 decimal);

       n = 15 is the number of years.


So, FV = 12000%2A%28%281%2B0.092%29%5E15-1%29%2F0.092%29 = 357917.24 dollars.


Then convert the todays' dollars into the future dollars at 2.5% inflation

     Debbie's cash in the future dollars = 357917.24%2F%281%2B0.025%29%5E15 = 247129.53 future dollars.    ANSWER

Solved.