Use Exponential Models in Applications Elise invests $4500 in an account that compounds interest monthly and earns 6%. How long will it take for her money to double?

Question
Exponential models
asked 2020-11-07
Use Exponential Models in Applications
Elise invests $4500 in an account that compounds interest monthly and earns 6%. How long will it take for her money to double?

Answers (1)

2020-11-08
Given:
\(\displaystyle{P}=\${4500}\)
\(\displaystyle{R}={6}\%\)
\(\displaystyle{A}=\${9000}\)
\(\displaystyle{n}=?\)
Since we are compounding monthly then we apply this formula
\(\displaystyle{A}={P}{\left({1}+{\frac{{{R}}}{{{12}{x}{100}}}}\right)}^{{{12}{n}}}\)
\(\displaystyle{9000}={4500}{\left({1}+{\frac{{{R}}}{{{12}{x}{100}}}}\right)}^{{{12}{n}}}\)
\(\displaystyle{2}={\left({1}+{.005}\right)}^{{{12}{n}}}{2}={1.005}^{{{12}{n}}}\)
Taking log on both side
\(\displaystyle{12}{n}{\log{{1.005}}}={\log{{2}}}\)
\(\displaystyle{12}{n}{x}{.0021}={0.301}\)
\(\displaystyle{n}={\frac{{{0.301}}}{{{0.026}}}}\)
\(\displaystyle{n}={11.57}\) years
0

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