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math

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The Concord Community Park Association receives a $10,000 donation from an anonymous donor who stipulates that before using the funds to improve the park, they must invest the money until it has doubled in value. The Park Association decides to invest the money in an account that pays 7%, compounded quarterly.

a. Write an equation that models the growth in value of the donation over time.
b. How many years will it take for the initial donation to double?

  • math -

    a. P = Po(1+r)^n.

    b. Po = $10,000 = Initial deposit.

    r = (7%/4)/100% = 0.0175 = Quarterly %
    rate expressed as a decimal.

    n = The # of compounding periods.

    P = 10000*(1.0175)^n = $20,000.
    (1.0175)^n = 2.0
    n*Log(1.0175) = Log2
    n = Log2/Log(1.0175)=40 Comp. periods.

    T = 40Comp. / 4comp./yr = 10 Years.

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