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=(0.69314718)/(0.0475)\\ \\ t=14.59\text{ years} \end{gathered}`

Therefore it will take 14.59 years to double the investment.