Step 1 :Recall the formula for the future value of an annuity: \(A = P \times \left(\frac{(1 + r/n)^{nt} - 1}{r/n}\right)\), where \(A\) is the end balance, \(P\) is the payment per period, \(r\) is the interest rate, \(t\) is the number of years, and \(n\) is the number of times the interest is compounded in a year.
Step 2 :Substitute the given information into the formula: \(P = 7000/16 = 437.5\), \(r = 0.067\), \(t = 4\), and \(n = 4\).
Step 3 :We have \(A = 437.5 \times \left(\frac{(1 + 0.067/4)^{4 \times 4} - 1}{0.067/4}\right)\).
Step 4 :Solving for \(A\) gives \(A = 7754.82\)..., which rounded to the nearest cent is \(\boxed{\$7754.82}\).