Let's analyze Roberto's assets and liabilities step-by-step to determine how the decision to use his investments to pay off his car loan will affect the difference between his assets and liabilities.
Step 1: Initial Totals
First, we sum up Roberto's initial assets and liabilities.
- Assets:
- Cash: [tex]$1,800
- Investments: $[/tex]6,200
- House: [tex]$150,000
- Car: $[/tex]8,000
Total initial assets:
[tex]\[
1,800 + 6,200 + 150,000 + 8,000 = 166,000
\][/tex]
- Liabilities:
- Credit card: [tex]$4,000
- Personal loan: $[/tex]1,000
- Mortgage: [tex]$100,000
- Car loan: $[/tex]5,000
Total initial liabilities:
[tex]\[
4,000 + 1,000 + 100,000 + 5,000 = 110,000
\][/tex]
- The initial difference (total assets - total liabilities):
[tex]\[
166,000 - 110,000 = 56,000
\][/tex]
Step 2: After Paying Off the Car Loan
Roberto uses [tex]$5,000 from his investments to pay off his car loan. We need to update the values for investments and the car loan:
- Assets (after paying off the car loan):
- Cash: $[/tex]1,800
- Investments: [tex]$6,200 - $[/tex]5,000 = [tex]$1,200
- House: $[/tex]150,000
- Car: [tex]$8,000
Total new assets:
\[
1,800 + 1,200 + 150,000 + 8,000 = 161,000
\]
- Liabilities (after paying off the car loan):
- Credit card: $[/tex]4,000
- Personal loan: [tex]$1,000
- Mortgage: $[/tex]100,000
- Car loan: [tex]$5,000 - $[/tex]5,000 = [tex]$0
Total new liabilities:
\[
4,000 + 1,000 + 100,000 + 0 = 105,000
\]
- The new difference (total new assets - total new liabilities):
\[
161,000 - 105,000 = 56,000
\]
Step 3: Comparing the Differences
- Initial difference between assets and liabilities: $[/tex]56,000
- New difference between assets and liabilities: $56,000
As seen, the difference between the assets and liabilities remains the same after Roberto uses his investments to pay off his car loan.
Thus, the correct conclusion is:
- The difference between the assets and the liabilities will remain the same.
