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Math Help - Find Annual Interest Rate

  1. #1
    MHF Contributor
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    Find Annual Interest Rate

    A business invests $10,000 in a savings account for two years. At the beginning of the second year, an additional $3500 is invested. At the end of the second year, the account balance is $15,569.75. What was the annual interest rate?

    Is there a formula?
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  2. #2
    Member jonah's Avatar
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    <br />
\begin{gathered}<br />
  10,000\left( {1 + i} \right)^2  + 3,500\left( {1 + i} \right) = 15,569.75 \hfill \\<br />
   \Leftrightarrow  \hfill \\ <br />
\end{gathered} <br />
    <br />
\begin{gathered}<br />
  \left[ {10,000\left( {1 + i} \right) + 3,500} \right]\left( {1 + i} \right) = 15,569.75 \hfill \\<br />
   \Leftrightarrow  \hfill \\ <br />
\end{gathered} <br />
    <br />
\begin{gathered}<br />
  \left[ {10,000 + 10,000i + 3,500} \right]\left( {1 + i} \right) = 15,569.75 \hfill \\<br />
   \Leftrightarrow  \hfill \\ <br />
\end{gathered} <br />
    <br />
10,000 + 10,000i + 3,500 + 10,000i + 10,000i^2  + 3,500i = 15,569.75<br />

    You need the quadratic formula.
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  3. #3
    MHF Contributor
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    ok....

    Quote Originally Posted by jonah View Post
    <br />
\begin{gathered}<br />
10,000\left( {1 + i} \right)^2 + 3,500\left( {1 + i} \right) = 15,569.75 \hfill \\<br />
\Leftrightarrow \hfill \\ <br />
\end{gathered} <br />
    <br />
\begin{gathered}<br />
\left[ {10,000\left( {1 + i} \right) + 3,500} \right]\left( {1 + i} \right) = 15,569.75 \hfill \\<br />
\Leftrightarrow \hfill \\ <br />
\end{gathered} <br />
    <br />
\begin{gathered}<br />
\left[ {10,000 + 10,000i + 3,500} \right]\left( {1 + i} \right) = 15,569.75 \hfill \\<br />
\Leftrightarrow \hfill \\ <br />
\end{gathered} <br />
    <br />
10,000 + 10,000i + 3,500 + 10,000i + 10,000i^2 + 3,500i = 15,569.75<br />

    You need the quadratic formula.
    Thank you.
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