Question

find the time it takes for \\$8,200 to double when invested at an annual interest rate of 9\\%, compounded continuously.
\text{ years}

find the time it takes for \\$820,000 to double when invested at an annual interest rate of 9\\%, compounded continuously.
\text{ years}

Explanation:

Step1: State the continuous compounding formula

$$A = P e^{rt}$$

Step2: Set up equation for doubling

$$2P = P e^{rt}$$

Step3: Simplify the equation

$$2 = e^{rt}$$

Step4: Solve for time \(t\)

$$t = \frac{\ln(2)}{r}$$

Step5: Calculate for \(r = 0.09\)

$$t = \frac{\ln(2)}{0.09} \approx 7.70$$

Answer:

7.70 years
7.70 years