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Math Help - investment question

  1. #1
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    investment question

    Tammy has joined a 401K plan with her company. Her goal is a total value of $2,000,000 when she retires in 45 years. With an expectant growth rate of 10% and being paid bi-weekly (26 times a year).

    What amount should she have deducted from her paycheck in order to meet her goal?
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  2. #2
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    Hello, Linda!

    Tammy has joined a 401K plan with her company.
    Her goal is a total value of $2,000,000 when she retires in 45 years.
    With an expectant growth rate of 10% and being paid bi-weekly (26 times a year),
    what amount should she have deducted from her paycheck in order to meet her goal?
    This is an Annuity . . .
    . . I will assume that the interest is computed bi-weekly.

    The formula is: . D \;=\;A\cdot\frac{i}{(1+i)^n-1}

    . . where: . \begin{Bmatrix}D &=&\text{periodic deposit} \\ A &=& \text{final amount} \\ i &=& \text{periodic interest rate} \\ n &=& \text{no. of periods} \end{Bmatrix}


    We have: . \begin{array}{ccc}A &=& 2,000,000 \\ i &=& \frac{0.1}{26} \\ n &=& 1170 \end{array}

    Hence: . D \;=\;2,000,000\cdot\frac{\frac{0.1}{26}}{\left(1 + \frac{0.1}{26}\right)^{1170} - 1} \;=\;87.17140754


    Therefore, Tammy should authorize an $87.17 bi-weekly deduction.


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

    Actually, she should authorize an $87.18 deduction.

    Rounding down, she will be about $32 short of her two million dollars.
    . . (But being a bi-millionaire at the time, she probably won't care.)

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