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,

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

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