Use the compound-interest formula to find the account balance $A$, where $P$ is principal, $r$ is interest rate, $n$ is number of compounding periods per year, $t$ is time, in years, and $A$ is account balance. \begin{tabular}{|c|c|c|c|} \hline $\mathrm{P}$ & $\mathrm{r}$ & compounded & $\mathrm{t}$ \\ \hline$\$ 59,458$ & $3 \frac{1}{2} \%$ & Quarterly & $3 \frac{1}{2}$ \\ \hline \end{tabular}

Step 1 ：Given the principal amount (P) is $59,458, the annual interest rate (r) is 3.5% or 0.035 in decimal form, the number of times that interest is compounded per year (n) is 4 (quarterly), and the time the money is invested for (t) is 3.5 years.

Step 2 ：We use the compound interest formula to find the account balance (A): \[A = P \left(1 + \frac{r}{n}\right)^{nt}\]

Step 3 ：Substitute the given values into the formula: \[A = 59458 \left(1 + \frac{0.035}{4}\right)^{4*3.5}\]

Step 4 ：Calculate the account balance: A = 67170.71402733811

Step 5 ：Round the account balance to two decimal places: \(\boxed{67170.71}\)