Question
You have four credit cards. Each has a balance of $450.00, but their credit limits are $800.00, $1,200.00, $1,300.00, and $1,500.00. Paying off and closing which card would decrease your debt ratio?
(1 point)
Responses
the $1,500.00 limit card
the $1,500.00 limit card
the $800.00 limit card
the $800.00 limit card
the $1,200.00 limit card
the $1,200.00 limit card
the $1,300.00 limit card
(1 point)
Responses
the $1,500.00 limit card
the $1,500.00 limit card
the $800.00 limit card
the $800.00 limit card
the $1,200.00 limit card
the $1,200.00 limit card
the $1,300.00 limit card
Answers
GPT-4o mini
To determine which card to pay off and close in order to decrease your debt ratio, you need to consider how debt ratio is calculated. The debt ratio is the total amount of outstanding debt divided by the total amount of available credit (credit limits).
In your case:
- Total Debt: $450.00 × 4 cards = $1,800.00
- Total Credit Limit: $800.00 + $1,200.00 + $1,300.00 + $1,500.00 = $3,800.00
**Current Debt Ratio:**
\[
\text{Debt Ratio} = \frac{Total Debt}{Total Credit Limit} = \frac{1,800.00}{3,800.00} \approx 0.474 (or 47.4\%)
\]
Now, let's analyze the effect of paying off and closing each card on the debt ratio:
1. **Closing the $1,500.00 limit card (balance $450.00)**:
- New Total Debt: $1,800.00 - $450.00 = $1,350.00
- New Total Credit Limit: $3,800.00 - $1,500.00 = $2,300.00
- New Debt Ratio: \(\frac{1,350.00}{2,300.00} \approx 0.587 (or 58.7\%)\)
2. **Closing the $1,200.00 limit card (balance $450.00)**:
- New Total Debt: $1,800.00 - $450.00 = $1,350.00
- New Total Credit Limit: $3,800.00 - $1,200.00 = $2,600.00
- New Debt Ratio: \(\frac{1,350.00}{2,600.00} \approx 0.519 (or 51.9\%)\)
3. **Closing the $1,300.00 limit card (balance $450.00)**:
- New Total Debt: $1,800.00 - $450.00 = $1,350.00
- New Total Credit Limit: $3,800.00 - $1,300.00 = $2,500.00
- New Debt Ratio: \(\frac{1,350.00}{2,500.00} = 0.54 (or 54\%)\)
4. **Closing the $800.00 limit card (balance $450.00)**:
- New Total Debt: $1,800.00 - $450.00 = $1,350.00
- New Total Credit Limit: $3,800.00 - $800.00 = $3,000.00
- New Debt Ratio: \(\frac{1,350.00}{3,000.00} = 0.45 (or 45\%)\)
**Conclusion**: Closing the **$800.00 limit card** will result in the lowest debt ratio, thus decreasing your debt ratio the most effectively.
So, the correct response is: **the $800.00 limit card.**
In your case:
- Total Debt: $450.00 × 4 cards = $1,800.00
- Total Credit Limit: $800.00 + $1,200.00 + $1,300.00 + $1,500.00 = $3,800.00
**Current Debt Ratio:**
\[
\text{Debt Ratio} = \frac{Total Debt}{Total Credit Limit} = \frac{1,800.00}{3,800.00} \approx 0.474 (or 47.4\%)
\]
Now, let's analyze the effect of paying off and closing each card on the debt ratio:
1. **Closing the $1,500.00 limit card (balance $450.00)**:
- New Total Debt: $1,800.00 - $450.00 = $1,350.00
- New Total Credit Limit: $3,800.00 - $1,500.00 = $2,300.00
- New Debt Ratio: \(\frac{1,350.00}{2,300.00} \approx 0.587 (or 58.7\%)\)
2. **Closing the $1,200.00 limit card (balance $450.00)**:
- New Total Debt: $1,800.00 - $450.00 = $1,350.00
- New Total Credit Limit: $3,800.00 - $1,200.00 = $2,600.00
- New Debt Ratio: \(\frac{1,350.00}{2,600.00} \approx 0.519 (or 51.9\%)\)
3. **Closing the $1,300.00 limit card (balance $450.00)**:
- New Total Debt: $1,800.00 - $450.00 = $1,350.00
- New Total Credit Limit: $3,800.00 - $1,300.00 = $2,500.00
- New Debt Ratio: \(\frac{1,350.00}{2,500.00} = 0.54 (or 54\%)\)
4. **Closing the $800.00 limit card (balance $450.00)**:
- New Total Debt: $1,800.00 - $450.00 = $1,350.00
- New Total Credit Limit: $3,800.00 - $800.00 = $3,000.00
- New Debt Ratio: \(\frac{1,350.00}{3,000.00} = 0.45 (or 45\%)\)
**Conclusion**: Closing the **$800.00 limit card** will result in the lowest debt ratio, thus decreasing your debt ratio the most effectively.
So, the correct response is: **the $800.00 limit card.**