Find the doubling time of an investment earning $4 \%$ interest if interest is compounded continuously.

Step 1 ：We are given an investment earning $4 \%$ interest compounded continuously and we are asked to find the doubling time of the investment.

Step 2 ：The formula for continuous compounding is \(A = Pe^{rt}\), where \(A\) is the final amount, \(P\) is the principal amount, \(r\) is the interest rate, and \(t\) is the time.

Step 3 ：In this case, we want to find the time it takes for the investment to double, so \(A = 2P\). We can substitute this into the formula and solve for \(t\).

Step 4 ：Given that the interest rate \(r = 0.04\), we can substitute this into the formula and solve for \(t\).

Step 5 ：Solving for \(t\), we get \(t = 17.328679513998633\).

Step 6 ：Rounding to two decimal places, we get \(t = 17.33\).

Step 7 ：Final Answer: The doubling time of an investment earning $4 \%$ interest if interest is compounded continuously is approximately \(\boxed{17.33}\) years.