contestada

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

Respuesta :

From the question,

We are given the

Rate = 5.84% = 0.0584

We will apply the formula

[tex]A=Pe^{rt}[/tex]

Since the Amount is double the principal

Then the equation becomes

[tex]\begin{gathered} 2P=Pe^{rt} \\ 2=e^{rt} \end{gathered}[/tex]

Substituting the value of r we get

[tex]2=e^{0.0584t}[/tex]

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

[tex]\begin{gathered} \ln 2=0.0584t \\ t=\frac{\ln 2}{0.0584} \\ t\approx11.87years \end{gathered}[/tex]

Therefore, the answer is 11.87 years

Otras preguntas