Answer :
To find the real investment value from a pretax return of \[tex]$5,000 given a state tax rate of 4.5% and a federal tax rate of 22.0%, we follow a systematic calculation process:
1. Calculate the State Tax:
\[
\text{State Tax} = \text{Pretax Return} \times \text{State Tax Rate}
\]
Given:
\[
\text{Pretax Return} = \$[/tex]5,000
\]
[tex]\[ \text{State Tax Rate} = 4.5\% = 0.045 \][/tex]
Therefore:
[tex]\[ \text{State Tax} = 5000 \times 0.045 = \$225.00 \][/tex]
2. Calculate the Federal Tax:
[tex]\[ \text{Federal Tax} = \text{Pretax Return} \times \text{Federal Tax Rate} \][/tex]
Given:
[tex]\[ \text{Federal Tax Rate} = 22.0\% = 0.22 \][/tex]
Therefore:
[tex]\[ \text{Federal Tax} = 5000 \times 0.22 = \$1,100.00 \][/tex]
3. Calculate the Total Tax:
[tex]\[ \text{Total Tax} = \text{State Tax} + \text{Federal Tax} \][/tex]
Therefore:
[tex]\[ \text{Total Tax} = 225.00 + 1100.00 = \$1,325.00 \][/tex]
4. Calculate the Real Investment Value:
[tex]\[ \text{Real Investment Value} = \text{Pretax Return} - \text{Total Tax} \][/tex]
Therefore:
[tex]\[ \text{Real Investment Value} = 5000 - 1325 = \$3,675.00 \][/tex]
Finally, comparing the calculated real investment value with the given choices, we find the correct answer is:
[tex]\[ \boxed{3,675} \][/tex]
\]
[tex]\[ \text{State Tax Rate} = 4.5\% = 0.045 \][/tex]
Therefore:
[tex]\[ \text{State Tax} = 5000 \times 0.045 = \$225.00 \][/tex]
2. Calculate the Federal Tax:
[tex]\[ \text{Federal Tax} = \text{Pretax Return} \times \text{Federal Tax Rate} \][/tex]
Given:
[tex]\[ \text{Federal Tax Rate} = 22.0\% = 0.22 \][/tex]
Therefore:
[tex]\[ \text{Federal Tax} = 5000 \times 0.22 = \$1,100.00 \][/tex]
3. Calculate the Total Tax:
[tex]\[ \text{Total Tax} = \text{State Tax} + \text{Federal Tax} \][/tex]
Therefore:
[tex]\[ \text{Total Tax} = 225.00 + 1100.00 = \$1,325.00 \][/tex]
4. Calculate the Real Investment Value:
[tex]\[ \text{Real Investment Value} = \text{Pretax Return} - \text{Total Tax} \][/tex]
Therefore:
[tex]\[ \text{Real Investment Value} = 5000 - 1325 = \$3,675.00 \][/tex]
Finally, comparing the calculated real investment value with the given choices, we find the correct answer is:
[tex]\[ \boxed{3,675} \][/tex]
