To determine which statement is correct, we will first calculate the total assets and liabilities for the Smith family in both 2005 and 2009. We will then compare the totals to see how they changed over this period.
Step 1: Calculate Total Assets in 2005 and 2009
- 2005 Assets:
- Home valued at \[tex]$200,000
- Car valued at \$[/tex]25,000
Total assets in 2005 = \[tex]$200,000 + \$[/tex]25,000 = \[tex]$225,000
- 2009 Assets:
- Home valued at \$[/tex]180,000
- Car valued at \[tex]$18,000
- Boat valued at \$[/tex]20,000
Total assets in 2009 = \[tex]$180,000 + \$[/tex]18,000 + \[tex]$20,000 = \$[/tex]218,000
Step 2: Calculate Total Liabilities in 2005 and 2009
- 2005 Liabilities:
- Mortgage of \[tex]$30,000
- Car loan of \$[/tex]8,000
Total liabilities in 2005 = \[tex]$30,000 + \$[/tex]8,000 = \[tex]$38,000
- 2009 Liabilities:
- Home equity loan of \$[/tex]18,000
- Personal loan of \[tex]$5,000
Total liabilities in 2009 = \$[/tex]18,000 + \[tex]$5,000 = \$[/tex]23,000
Step 3: Determine Changes in Assets and Liabilities
- Change in Assets:
- Total assets in 2009: \[tex]$218,000
- Total assets in 2005: \$[/tex]225,000
Change in assets = \[tex]$218,000 - \$[/tex]225,000 = -\[tex]$7,000
The assets decreased by \$[/tex]7,000.
- Change in Liabilities:
- Total liabilities in 2009: \[tex]$23,000
- Total liabilities in 2005: \$[/tex]38,000
Change in liabilities = \[tex]$23,000 - \$[/tex]38,000 = -\[tex]$15,000
The liabilities decreased by \$[/tex]15,000.
Conclusion:
- From 2005 to 2009, the assets of the Smith family decreased.
- From 2005 to 2009, the liabilities of the Smith family also decreased.
Therefore, the correct statement is:
a. From 2005 to 2009, both assets and liabilities decreased.
So, the best answer is option (a).
