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$1750 is invested in an account earning 3.5% interest compounded annualy. How long will it need to be in an account to double?

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Given :


\begin{gathered} P\text{ = \$ 1750} \\ R\text{ = 3.5 \%} \\ A\text{ = 2P} \\ A\text{ = 2}*\text{ 1750 = \$ 3500} \end{gathered}

Amount is given as,


\begin{gathered} A\text{ = P( 1 + }(R)/(100))^T \\ 3500\text{ = 1750( 1 + }(3.5)/(100))^T \\ \text{( 1 + }(3.5)/(100))^T\text{ = }(3500)/(1720) \end{gathered}

Further,


\begin{gathered} \text{( 1 + }(3.5)/(100))^T\text{ = 2} \\ ((103.5)/(100))^T\text{ = }2 \\ (1.035)^T\text{ = 2} \end{gathered}

Taking log on both the sides,


\begin{gathered} \log (1.035)^T\text{ = log 2} \\ T\log (1.035)\text{ = log 2} \\ T\text{ = }\frac{\log \text{ 2}}{\log \text{ 1.035}} \end{gathered}

Therefore,


\begin{gathered} T\text{ = }(0.3010)/(0.0149) \\ T\text{ = 20.20 years }\approx\text{ 20 years} \end{gathered}

Thus the required time is 20 years.

User Esmie
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