Suppose that $$13,000$ is invested in a bond fund and the account grows to $$14,772\mathrm{.}63$ in $3yr.$

Part $1$ of $2$

$($a$)$ Use the model $A=P{e}^{rt}$ to determine the average tate of return under continuous compounding. Round to the nearest tenth of a percent. Avoid rounding in intermediate steps.

The average rate of return under continuous compounding is approximately

$\%.$

Part: $\frac{1}{2}$

Part $2$ of $2$

$($b$)$ How long will it take the investment to reach $$22,000$ if the rate of return continues? Round to the nearest tenth of a year. Round values in intermediate steps to three decimal places.

It will take the investment approximately yr to reach $$22,000$ if the rate of return continues.