How long will it take for a $\$ 3000$ investment to grow to $\$ 4335$ at an annual rate of $4 \%$, compounded quarterly? Assume that no withdrawals are made. Do not round any intermediate computations, and round your answer to the nearest hundredth. years

Step 1 ：To solve for the time it takes for an investment to grow at a compounded interest rate, we use the formula \( A = P(1 + \frac{r}{n})^{nt} \)

Step 2 ：Given values: \( A = \$4335 \), \( P = \$3000 \), \( r = 4\% = 0.04 \), \( n = 4 \) (compounded quarterly)

Step 3 ：Substitute the given values into the formula: \( 4335 = 3000(1 + \frac{0.04}{4})^{4t} \)

Step 4 ：Solve for \( t \) using algebraic methods

Step 5 ：After calculations, we find that \( t = 9.25 \) years

Step 6 ：Final Answer: \( \boxed{9.25} \)