Which is a better way to invest $\$ 7000$ if the concern is simply the future value: a 4-year certificate of deposit paying $2.2 \%$ compounded quarterly, or a 4 -year annuity that divides that $\$ 7000$ into 16 quarterly payments and pays $6.7 \%$ compounded quarterly? Round your answers to the nearest cent.
Part 1 of 3
The 4-year certificate of deposit has a future value of $\$ 7,642.07$.
Part: $1 / 3$
Part 2 of 3
The 4 -year annuity has a future value of $\$ \square$.
$\times \quad 5$

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 \(\boxed{\$7754.82}\).