1. **State the problem:** We want to find the annual percentage rate $r$ for an account where money is deposited and the interest is compounded continuously, given that the balance doubles in 6 years. 2. **Formula used:** The formula for continuous compounding is: $$ A = P e^{rt} $$ where: - $A$ is the amount after time $t$, - $P$ is the principal (initial amount), - $r$ is the annual interest rate (as a decimal), - $t$ is the time in years, - $e$ is Euler's number (approximately 2.71828). 3. **Apply the problem conditions:** Since the balance doubles, $A = 2P$, and $t = 6$ years. 4. **Set up the equation:** $$ 2P = P e^{6r} $$ 5. **Divide both sides by $P$ to simplify:** $$ \frac{2P}{\cancel{P}} = \frac{P e^{6r}}{\cancel{P}} \implies 2 = e^{6r} $$ 6. **Take the natural logarithm of both sides:** $$ \ln(2) = \ln\left(e^{6r}\right) = 6r $$ 7. **Solve for $r$:** $$ r = \frac{\ln(2)}{6} $$ 8. **Calculate the numerical value:** $$ r \approx \frac{0.6931}{6} \approx 0.1155 $$ 9. **Convert to percentage:** $$ 0.1155 \times 100 = 11.55\% $$ **Final answer:** The annual percentage rate is approximately **11.55%**.