Sure, let's determine the maximum contribution to a Keogh plan for different scenarios of self-employment income.
### Problem Analysis
A Keogh plan allows self-employed individuals to save for retirement with tax-deferred contributions. The maximum contribution to a Keogh plan is typically calculated as 20% of self-employment income.
### Case Breakdown
#### a. Self-employment income of \[tex]$71,000
The maximum contribution is calculated as 20% of \$[/tex]71,000.
[tex]\[ \text{Maximum Keogh plan contribution} = 0.20 \times 71,000 = 14,200 \][/tex]
So, the maximum Keogh plan contribution for this case is \[tex]$14,200.
#### b. Self-employment income of \$[/tex]71,000 and wage income of \[tex]$30,000
Here, the individual also has a wage income, but wage income does not affect the Keogh plan contribution for self-employment income. Hence, we only consider the self-employment income of \$[/tex]71,000 and compute 20% of it.
[tex]\[ \text{Maximum Keogh plan contribution} = 0.20 \times 71,000 = 14,200 \][/tex]
So, the maximum Keogh plan contribution for this case remains the same at \[tex]$14,200.
#### c. Self-employment income of \$[/tex]125,000
The maximum contribution is calculated as 20% of \[tex]$125,000.
\[ \text{Maximum Keogh plan contribution} = 0.20 \times 125,000 = 25,000 \]
So, the maximum Keogh plan contribution for this case is \$[/tex]25,000.
#### d. Self-employment income of \[tex]$355,000
The maximum contribution is calculated as 20% of \$[/tex]355,000.
[tex]\[ \text{Maximum Keogh plan contribution} = 0.20 \times 355,000 = 71,000 \][/tex]
So, the maximum Keogh plan contribution for this case is \[tex]$71,000.
### Summary Table
\[
\begin{array}{|l|c|}
\hline
\text{Case} & \text{Maximum Keogh Plan Contribution (\$[/tex]}) \\
\hline
a. & 14,200 \\
\hline
b. & 14,200 \\
\hline
c. & 25,000 \\
\hline
d. & 71,000 \\
\hline
\end{array}
\]
So, in summary:
- The maximum contribution for [tex]\( a \)[/tex] (self-employment income of [tex]$71,000) is \$[/tex]14,200.
- The maximum contribution for [tex]\( b \)[/tex] (self-employment income of [tex]$71,000 and wage income of $[/tex]30,000) is \[tex]$14,200.
- The maximum contribution for \( c \) (self-employment income of $[/tex]125,000) is \[tex]$25,000.
- The maximum contribution for \( d \) (self-employment income of $[/tex]355,000) is \$71,000.
