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=(\ln 2)/(0.0584) \\ t\approx11.87years \end{gathered}`

Therefore, the answer is 11.87 years