Question

Do not round any intermediate computations, and round your answer to the nearest hundredth

Answer 1

In order to calculate continuous interest, we can use the formula below:

$A=Pe^{rt}$

Where A is the amount after t years, P is the principal (initial value) and r is the interest rate.

So, using A = 2P and r = 0.0475, we have:

$\begin{gathered} 2P=Pe^{0.0475t}\\ \\ 2=e^{0.0475t}\\ \\ \ln e^{0.0475t}=\ln2\\ \\ 0.0475t=0.69314718\\ \\ t=\frac{0.69314718}{0.0475}\\ \\ t=14.59\text{ years} \end{gathered}$

Therefore it will take 14.59 years to double the investment.