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 1207421: 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?
Answer by ikleyn(52784) About Me  (Show Source):
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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.