To determine the college graduate's new net worth, we need to follow a systematic approach, analyzing the initial assets and liabilities, incorporating the signing bonus and the student loan payoff, and then calculating the new net worth.
### Step 1: Calculate Initial Assets
We start by adding up all the assets:
1. Furniture: [tex]$4,091
2. Savings Account Balance: $[/tex]2,143
3. Car Value: [tex]$21,500
4. Equipment: $[/tex]4,805
So, the total initial assets are:
[tex]\[ 4,091 + 2,143 + 21,500 + 4,805 = 32,539 \][/tex]
### Step 2: Calculate Initial Liabilities
Next, we sum up all the liabilities:
1. Car Loan: [tex]$6,060
2. Credit Card Balances: $[/tex]3,940
3. Student Loans: [tex]$29,400
So, the total initial liabilities are:
\[ 6,060 + 3,940 + 29,400 = 39,400 \]
### Step 3: Calculate Initial Net Worth
Net worth is calculated as:
\[ \text{Net Worth} = \text{Total Assets} - \text{Total Liabilities} \]
Substituting the values:
\[ \text{Net Worth} = 32,539 - 39,400 = -6,861 \]
### Step 4: Update Assets with the Signing Bonus
The graduate receives a $[/tex]10,000 signing bonus, which increases the savings account balance:
[tex]\[ \text{New Savings Account Balance} = 2,143 + 10,000 = 12,143 \][/tex]
Now, the new total assets are:
[tex]\[ 4,091 + 12,143 + 21,500 + 4,805 = 42,539 \][/tex]
### Step 5: Update Liabilities with the Student Loan Payoff
The firm pays off [tex]$25,000 of the student loans:
\[ \text{Remaining Student Loans} = 29,400 - 25,000 = 4,400 \]
The new total liabilities are:
\[ 6,060 + 3,940 + 4,400 = 14,400 \]
### Step 6: Calculate New Net Worth
Finally, the new net worth is:
\[ \text{New Net Worth} = \text{New Total Assets} - \text{New Total Liabilities} \]
Substituting the values:
\[ \text{New Net Worth} = 42,539 - 14,400 = 28,139 \]
### Conclusion
The college graduate's new net worth is $[/tex]28,139, which corresponds to the last option:
[tex]\[
\boxed{28,139}
\][/tex]
