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algebra

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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 - ,

    What is the monthly deposit required to accumulate to a fund of $1,000,000 over a period of 40 years with deposits starting at the end of the first month and bearing an interest rate of 8% compounded monthly?

    S(n) = $1,000,000]
    i = .08/12 = .00666...
    n = 40(12) = 48

    R = S(n)(i)/[(1+i)^n - 1]
    1,000,000(.00666...)/[1.00666...)^48-1]
    $17,746.25

    As for the present value,

    P = R[1 - (1+i)^-n]/i

    P=17,746.25[1-(1.00666...)^-40]/.00666...
    P = $726,920.

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