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Math Help - Brain Buster

  1. #1
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    Question Brain Buster

    Here is a Brain buster ( at least to me or else I wouldn't be on here right now)

    Suppose you have children young, pay for their college expenses, and finally start saving for retirement at age 45. How much do you have to save per month with a steady return of 7.5% monthly to accumulate $250,000 by 65?
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  2. #2
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    Hello, Ashley!

    Suppose you start saving for retirement at age 45.
    How much do you have to save per month with a steady return
    of 7.5% monthly (?) to accumulate $250,000 by 65?
    I seriously doubt that 7.5% is a monthly rate.
    . . I'll assume it is an annual rate.

    This is an Annuity problem and has its own formula: . D \;=\;A\,\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: . A = \$250,000,\;\;i = \frac{7.5\%}{12} = 0.00625\text{ per month},\;\;n = 240\text{ months}

    Hence: . D \;=\;250,000\,\frac{0.00625}{(1.00625)^{240} - 1} \;=\;451.4829830


    Therefore, we should save about $451.48 per month.

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