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Math Help - Don't Have A Clue!!

  1. #1
    steph
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    Don't Have A Clue!!

    Financial Math

    How much should be invested at 8% compounded semiannually in order to have $5000 at the end of 8 years?
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  2. #2
    Super Member

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    Hello, steph!

    You're expected to know the compound interest formula:

    . . A \;= \;P(1 + i)^m

    . . where: . \begin{array}{cccc} a\:= \\ P\:= \\ i\:=\\n\:=\end{array}<br />
\begin{array}{cccc}\text{final amount} \\ \text{principal invested} \\ \text{periodic interest rate} \\ \text{number of periods}\end{array}


    How much should be invested at 8% compounded semiannually
    in order to have $5000 at the end of 8 years?

    We are given: . \begin{array}{ccc}A\:= \\ i\:= \\ n\:=\end{array}<br />
\begin{array}{ccc}5000 \\ 8\%/2 = 0.04 \\ 2\times8 = 16\end{array}

    So we have: . 5000 \;=\;P(1+0.02)^{16}

    Then: . P \;= \;\frac{5000}{(1.02)^{16}} \;=\; 3642.229069

    Therefore, \$3,642.23 should be invested.

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