Over the period of a year, Julie's net worth decreased. Which of the following could be true?
A. Julie's assets and liabilities decreased by the same amount.
B. Julie's assets and liabilities increased by the same amount.
C. Julie's assets increased by more than her liabilities.
D. Julie's assets decreased by more than her liabilities.
Answer (1)
Define net worth as A sse t s − L iabi l i t i es and analyze the change in net worth.
If assets and liabilities change by the same amount, net worth remains constant.
If assets increase more than liabilities, net worth increases.
If assets decrease more than liabilities, net worth decreases, which matches the problem statement. Therefore, the answer is d .
Explanation
Understanding the Problem Let's analyze the problem. Julie's net worth decreased over a year. We need to determine which of the given scenarios could be true. Net worth is defined as the difference between assets and liabilities: N e t W or t h = A sse t s − L iabi l i t i es . A decrease in net worth means that the change in net worth is negative.
Defining Variables and Net Worth Change Let A 1 and L 1 be the initial assets and liabilities, respectively, and A 2 and L 2 be the final assets and liabilities, respectively. The change in net worth is given by Δ N e t W or t h = ( A 2 − L 2 ) − ( A 1 − L 1 ) = ( A 2 − A 1 ) − ( L 2 − L 1 ) . Since Julie's net worth decreased, Δ N e t W or t h < 0 , which means ( A 2 − A 1 ) − ( L 2 − L 1 ) < 0 .
Analyzing Each Option Now, let's analyze each option: a) Assets and liabilities decreased by the same amount: A 2 − A 1 = − x and L 2 − L 1 = − x , where 0"> x > 0 . Then Δ N e t W or t h = − x − ( − x ) = 0 . This contradicts the given information that net worth decreased. b) Assets and liabilities increased by the same amount: A 2 − A 1 = x and L 2 − L 1 = x , where 0"> x > 0 . Then Δ N e t W or t h = x − x = 0 . This contradicts the given information that net worth decreased. c) Assets increased by more than her liabilities: L_2 - L_1"> A 2 − A 1 > L 2 − L 1 , which means 0"> ( A 2 − A 1 ) − ( L 2 − L 1 ) > 0 . This contradicts the given information that net worth decreased. d) Assets decreased by more than her liabilities: A 2 − A 1 < L 2 − L 1 , which means ( A 2 − A 1 ) − ( L 2 − L 1 ) < 0 . This is consistent with the given information that net worth decreased.
Conclusion Therefore, the correct answer is d.
Examples
Understanding the relationship between assets, liabilities, and net worth is crucial in personal finance. For example, if you're considering buying a house (an asset) but taking on a large mortgage (a liability), it's important to ensure that the asset's value doesn't decrease faster than you pay off the mortgage. If it does, your net worth will decrease, potentially putting you in a financially precarious situation. This principle applies to businesses as well, where managing assets and liabilities effectively is key to maintaining a healthy financial position.
