Suppose that $\$ 4000$ is placed in a savings account at an annual rate of $7 \%$, compounded quarterly. Assuming that no withdrawals are made, how loing will it take for the account to grow to $\$ 5372$ ? Do not round any intermediate computations, and round your answer to the nearest hundredth.

Step 1 ：Given that the principal amount (P) is $4000, the final amount (A) is $5372, the annual interest rate (r) is 7% or 0.07 in decimal, and the interest is compounded quarterly (n=4).

Step 2 ：We can use the formula for compound interest, rearranged to solve for time (t): \(t = \frac{\log(\frac{A}{P})}{n \cdot \log(1 + \frac{r}{n})}\)

Step 3 ：Substitute the given values into the formula: \(t = \frac{\log(\frac{5372}{4000})}{4 \cdot \log(1 + \frac{0.07}{4})}\)

Step 4 ：Solving the equation gives us \(t \approx 4.249698331550322\)

Step 5 ：Rounding to the nearest hundredth, we get \(t \approx 4.25\)

Step 6 ：Final Answer: The time it will take for the account to grow to $5372 is approximately \(\boxed{4.25}\) years.