Problem

The value of an account that is being compounded continuously is given by the formula $A=P e^{r \prime}$, where $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years. Approximately how long will it take for the amount of money to double if the interest rate is $2.4 \%$ ?
11.0 years
12.9 years
20.0 years
28.9 years

Answer

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Answer

\(\boxed{28.9}\) years

Steps

Step 1 ：Set up the equation: \(2P = Pe^{0.024t}\)

Step 2 ：Solve for t: \(t = \frac{\ln(2)}{0.024}\)

Step 3 ：Calculate t: \(t \approx 28.9\)

Step 4 ：\(\boxed{28.9}\) years

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