How much must be deposited at the end of every three months for 9.5 years to accumulate to $\$ 2639.00$ at $7 \%$ compounded quarterly?
The required deposit is $\$$ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed. $)^{\circ}$

Step 1 ：We are given a problem of future value of an ordinary annuity. The formula for future value of an ordinary annuity is: \(FV = P \times \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}}\) where: FV = future value, P = payment per period, r = annual interest rate (in decimal), n = number of compounding periods per year, t = time in years.

Step 2 ：In this case, we know: FV = $2639, r = 7% = 0.07, n = 4 (quarterly compounding), t = 9.5 years. We need to solve for P.

Step 3 ：Rearranging the formula, we get: \(P = FV \times \frac{\frac{r}{n}}{(1 + \frac{r}{n})^{nt} - 1}\)

Step 4 ：Substituting the known values into the formula, we get: \(P = 2639 \times \frac{\frac{0.07}{4}}{(1 + \frac{0.07}{4})^{4 \times 9.5} - 1}\)

Step 5 ：Solving the equation, we get: P = 49.480980656643354

Step 6 ：Rounding the final answer to the nearest cent, we get: \(\boxed{\$49.48}\)