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Math Help - Impossible Interest question.

  1. #1
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    Impossible Interest question.

    At the end of each quarter year, aaron makes a 625 payment into a mutual fund that earns an annual percentage rate of 6%, compounded quarterly. The future value, of aaron's investment is = FV= R[(1+i)^n -1] / i - where n is the number of equal periodic payments of R dollars, and i is the interest rate per compounding period expressed as a decimal. After how long will aaron's investment be worth 1 million?

    I did 625 [(1.015^4x)-1] / .015 - wasnt right, tried all variations of 1.06 and 4x, x 1/4x , didnt get it.

    Answer s 54.25 years, i got close tho at 54.05 years. But nope, not good enough, if ex. it was a numerical response i would get it wrong still.

    Anyone know how to do this, and see what i did wrong?
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  2. #2
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    Re: Impossible Interest question.

    Hello, skg94!

    Your intentions were honorable.
    You must have made some elementary errors.


    At the end of each quarter-year, Aaron makes a $625 payment into a mutual fund
    that earns an annual percentage rate of 6%, compounded quarterly.
    The future value, of aaron's investment is: . FV \:=\: R\frac{(1+i)^n -1}{i}
    . . where n = number of equal periodic payments of R dollars,
    . . and i = interest rate per period.
    After how long will aaron's investment be worth 1 million dollars?

    We have: . FV \,=\, 1,\!000,\!000,\;\;R \,=\,625,\;\; i \,=\, \tfrac{6\%}{4} \,=\, 0.015

    Substitute: . 625\,\frac{1.015^n - 1}{0.015} \:=\:1,\!000,\!000

    . . . . . . . . . 1.015^n - 1 \:=\:24 \quad\Rightarrow\quad 1.015^n \:=\:25

    Take logs: . \ln(1.015^n) \:=\:\ln(25) \quad\Rightarrow\quad n\!\cdot\!\ln(1.015) \:=\:\ln(25)

    Hence: . n \;=\;\frac{\ln(25)}{\ln(1.015)} \;=\; 216.1971659


    \text{Therefore, it will take }217\text{ quarters }=\: 54\tfrac{1}{4}\text{ years.} .**


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    ** . \text{If }n = 216\text{, he will have "only" }\$996,946.64
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