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Math Help - Investment Problem find rate

  1. #1
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    Investment Problem find rate

    $6000 is deposited into an account. It grows to $10000 in 8 years. What is the interest rate assuming an annual compound?

    I'm not exactly sure what to do please help!
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  2. #2
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    Hello, civiliam!

    $6000 is deposited into an account. It grows to $10000 in 8 years.
    What is the interest rate assuming an annual compound?
    You're expected to know the compound interest formula: . A \;=\;P(1 + i)^n

    . . where: . \begin{Bmatrix}P &=& \text{principal deposited} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \\ A &=& \text{Final balance} \end{Bmatrix}


    We are given: . P = 6,\!000,\;\;n =8,\;\;A =10,\!000

    The equation becomes: . 10,\!000 \;=\;6,\!000(1+i)^8 \quad\Rightarrow\quad (1+i)^8 \:=\:\frac{10,\!000}{6,\!000} \:=\:\frac{5}{3}

    Take the 8th root of both sides: . 1 + i \:=\:\left(\frac{5}{3}\right)^{\frac{1}{8}} \quad\Rightarrow\quad i \:=\:\left(\frac{5}{3}\right)^{\frac{1}{8}} - 1


    Therefore: . i \;=\;0.065935911 \;\approx\;6.6\%

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  3. #3
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    life saver thanks so much
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