What is the interest rate necessary for an investment to quadruple after 14 years of continuous compound interest?
\[
r=\square \%
\]
(Round to two decimal places as needed.)

Step 1 ：We are given that the investment quadruples after 14 years of continuous compound interest. This means that the final amount (A) is four times the principal amount (P). We can represent this as A = 4P.

Step 2 ：We are asked to find the interest rate (r) necessary for this to happen. We can use the formula for continuous compound interest, which is A = P * e^(rt), where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years.

Step 3 ：Substituting the given values into the formula, we get 4 = e^(14r).

Step 4 ：To solve for r, we first take the natural logarithm of both sides of the equation to get ln(4) = 14r.

Step 5 ：Dividing both sides of the equation by 14, we get r = ln(4) / 14.

Step 6 ：Calculating the value of r, we get r ≈ 0.09902102579427789.

Step 7 ：Converting this to a percentage, we get r ≈ 9.9%.

Step 8 ：Final Answer: The interest rate necessary for an investment to quadruple after 14 years of continuous compound interest is \(\boxed{9.9\%}\).