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Math Help - Interest Problem

  1. #1
    Junior Member
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    Red face Interest Problem

    this is out of my chapter with exponential and logarithmic functions

    Use the compound interest formulas
    A=P(1 + r over n)^nt and A=Pe^rt

    Suppose that you have $14,000 to invest. Which investment yields the greater return over 10 years: 7% compounded monthly or 6.85% compounded continuously?
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  2. #2
    Super Member

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    Hello, kbryant05!

    Exactly where is your difficulty?
    . . You were sick for a week and missed all the lectures?
    . . You don't know how to use those formulas?
    . . You can't plug the stuff into your calculator?

    Use the compound interest formulas: A\:=\:P\left(1 + \frac{r}{n}\right)^{nt} and A\:=\:Pe^{rt}

    Suppose that you have $14,000 to invest.
    Which investment yields the greater return over 10 years:
    (a) 7% compounded monthly or (b)6.85% compounded continuously?
    (a) 7% compounded monthly for 10 years.
    We have: P = 14,000,\;\;r = 7\% = 0.07,\;\;n = 12,\;\;t = 10

    Then: A \;=\;14,000\left(1 + \frac{0.07}{12}\right)^{120} \;= \;28,135.25927\;\approx\;\$28,135.26


    (b) 6.85% compounded continuously for 10 years.
    We have: r = 6.85\% = 0.0685,\;\;t = 10

    Then: A\;=\;14,000e^{(0.0685)(10)}\;=\;27,772.8057\: \approx\;\$27,772.81


    Therefore, option (a) has the greater return.
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