a. Use the appropriate formula to find the value of the annuity.
b. Find the interest.
\begin{tabular}{|l|l|l|}
\hline Periodic Deposit & Rate & Time \\
\hline$\$ 120$ at the end of every six months & $4.5 \%$ compounded semiannually & 35 years \\
\hline
\end{tabular}
(i) Click the icon to view some finance formulas.
a. The value of the annuity is $\$$
(Do not round until the final answer. Then round to the nearest dollar as needed.)
b. The interest is $\$$
(Use the answer from part (a) to find this answer. Round to the nearest dollar as needed.)

Step 1 ：Given the periodic deposit (P) is $120, the annual interest rate (r) is 4.5% or 0.045 in decimal form, the number of times interest is compounded per year (n) is 2, and the number of years (t) is 35.

Step 2 ：First, we calculate the future value of the annuity (FV) using the formula: \(FV = P \times \left[(1 + \frac{r}{n})^{nt} - 1\right] \div \frac{r}{n}\)

Step 3 ：Substitute the given values into the formula: \(FV = 120 \times \left[(1 + \frac{0.045}{2})^{2 \times 35} - 1\right] \div \frac{0.045}{2}\)

Step 4 ：Calculate the future value to get: \(FV = 19984.75410998469\)

Step 5 ：Round the future value to the nearest dollar to get: \(FV = \$19985\)

Step 6 ：Next, calculate the total amount of deposits over the 35 years: \(total\_deposits = P \times n \times t = 120 \times 2 \times 35 = \$8400\)

Step 7 ：Finally, calculate the interest by subtracting the total deposits from the future value: \(interest = FV - total\_deposits = 19985 - 8400 = 11584.75410998469\)

Step 8 ：Round the interest to the nearest dollar to get: \(interest = \$11585\)

Step 9 ：\(\boxed{\text{The value of the annuity is \$19985 and the interest is \$11585.}}\)