Question

Find the amount of time required to double an amount at 5.84% if the interest is compounded continuously. 1) 5.15 years2) 5.94 years3) 11.87 years4) 23.74 years

Answer 1

From the question,

We are given the

Rate = 5.84% = 0.0584

We will apply the formula

$A=Pe^{rt}$

Since the Amount is double the principal

Then the equation becomes

$\begin{gathered} 2P=Pe^{rt} \\ 2=e^{rt} \end{gathered}$

Substituting the value of r we get

$2=e^{0.0584t}$

Next, we solve for t by taking ln of both sides

$\begin{gathered} \ln 2=0.0584t \\ t=\frac{\ln 2}{0.0584} \\ t\approx11.87years \end{gathered}$

Therefore, the answer is 11.87 years