QuestionHow long does it take for an investment to double in value if it is invested at $7 \%$ compounded monthly? Compounded continuously?
At 7\% compounded monthly, the investment doubles in about (Round to two decimal places as needed.) $\square$ years.

Studdy Solution
Solve for $t$ by taking the natural logarithm of both sides:
$$\ln(2) = 0.07t$$
Solve for $t$:
$$t = \frac{\ln(2)}{0.07}$$
Calculate $t$ using a calculator:
$$t \approx \frac{0.693147}{0.07} \approx 9.90$$
At 7% compounded continuously, the investment doubles in about $\boxed{9.90}$ years.