Question

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

Answer 1

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.