To find the future value of an annuity:

Dan invests [tex]$\$[/tex]1228[tex]$ every year in an annuity that pays $[/tex]6\%[tex]$ interest, compounded annually. Payments are made at the end of each year. Find the total value of the annuity in 20 years.

Do not round any intermediate computations, and round your final answer to the nearest cent.

Financial Formulas:
\[ A = P\left(1 + \frac{r}{n}\right)^{nt} \]
\[ A = \frac{M\left[\left(1 + \frac{r}{n}\right)^{nt} - 1\right]}{\frac{r}{n}} \]
\[ I = Prt \]
\[ A = Pe^{rt} \]

Where:
- \( P \) = principal
- \( A \) = future value or amount accumulated
- \( r \) = annual interest rate
- \( t \) = time or term of investment or loan (in years)
- \( n \) = number of times interest is compounded per year
- \( e \) = Euler's number
- \( M \) = installment payment or monthly payment
- \( Y \) = effective annual interest rate or effective annual yield

Given:
- Annual investment (\( M \)) = $[/tex]\[tex]$1228$[/tex]
- Interest rate ([tex]\( r \)[/tex]) = [tex]$6\%$[/tex] or [tex]$0.06$[/tex]
- Time ([tex]\( t \)[/tex]) = 20 years
- Compounded annually ([tex]\( n \)[/tex]) = 1

Compute:
[tex]\[ A = \frac{1228 \left[\left(1 + \frac{0.06}{1}\right)^{1 \times 20} - 1\right]}{\frac{0.06}{1}} \][/tex]

[tex]\[ A = \$45188.56 \][/tex]