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algebra

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3. Suppose a student wants to be a millionaire in 40 years. If she has an account that pays 8% interest compounded monthly, how much must she deposit each month in order to achieve her goal of having $1,000,000? What is the present value of this annuity?

  • algebra - ,

    P(1+.08/12)^40 = 1000000
    P*21.72 = 1000000
    P = $46040.52

  • algebra - ,

    Oops. Monthly deposits.

    Let r = 1 + .08/12 = 1.00666666

    M (r^480 - 1)/(r-1) = 1000000
    3641.007M = 1000000
    M = $274.65

    Anyone see an error here?

  • algebra - ,

    Steve, your method is correct,
    I let my calculator carry its maximum digits and got
    $286.45

    Also the present value of $1000000 40 years from now at 8% compounded monthly
    PV (1.00666666..)^480 = 1000000
    PV = $41197.40

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