To determine the real investment value given a pretax return of \[tex]$5,000, a state tax rate of 4.5%, and a federal tax rate of 22%, follow these steps:
1. Calculate the state tax:
- The state tax rate is 4.5%, or 0.045 in decimal form.
- To find the state tax, multiply the pretax return by the state tax rate:
\[
\text{State Tax} = \$[/tex]5,000 \times 0.045 = \[tex]$225
\]
2. Calculate the federal tax:
- The federal tax rate is 22%, or 0.22 in decimal form.
- To find the federal tax, multiply the pretax return by the federal tax rate:
\[
\text{Federal Tax} = \$[/tex]5,000 \times 0.22 = \[tex]$1,100
\]
3. Calculate the total tax:
- Add the state tax and the federal tax:
\[
\text{Total Tax} = \$[/tex]225 + \[tex]$1,100 = \$[/tex]1,325
\]
4. Calculate the real investment value:
- Subtract the total tax from the pretax return:
[tex]\[
\text{Real Investment Value} = \$5,000 - \$1,325 = \$3,675
\][/tex]
Therefore, the real investment value is [tex]$3,675$[/tex].
So, the correct answer is:
[tex]\[
\boxed{\$ 3,675}
\][/tex]
