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You invest $\$2,000$ in a savings account that offers an annual interest rate of $5\%$, compounded annually. How long will it take for your investment to grow to $\$3,000$$?$ $\newline$Use the formula $A = P\left(1 + \frac{r}{n}\right)^{nt}$, where $A$ is the balance (final amount), $P$ is the principal (starting amount), $r$ is the interest rate expressed as a decimal, $n$ is the number of times per year that the interest is compounded, and $t$ is the time in years. $\newline$Round your answer to the nearest hundredth.