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Please help! The amount of money in an account with continuously compounded interest

Please help! The amount of money in an account with continuously compounded interest-example-1
User Aherrick
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1 Answer

12 votes
12 votes

Given the formula


A=Pe^(rt)

Set


\begin{gathered} A=2P,r=3.4\%=0.034 \\ \Rightarrow2P=Pe^(0.034t) \\ \Rightarrow2=e^(0.034t) \end{gathered}

Then, solving for t,


\begin{gathered} \Rightarrow ln2=0.034t*ln(e)=0.034t \\ \Rightarrow t=(ln(2))/(0.034)\approx20.3867\approx20.4 \end{gathered}

Therefore, the answer is 20.4 years, the third option.

User Tkinter Lover
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