- First, identify eligibility by checking if savings meet the \(20\%\) down payment requirement, which disqualifies Person C.
- Calculate the monthly income for eligible candidates: A (\(\$4,250\)), B (\(\$4,833.33\)), and D (\(\$5,583.33\)).
- Determine the debt-to-income (DTI) ratio for each: Person A (\(\approx 0.0824\)), Person B (\(\approx 0.0517\)), and Person D (\(\approx 0.0806\)).
- Select Person B as the highest-rated applicant due to the lowest DTI ratio among those eligible: \(\boxed{b}\).
Explanation
- Problem Analysis and Methodology
To determine the highest-rated applicant for a home loan, we must first verify if each person meets the minimum down payment requirement of \(20\%\) of the home's value. Then, for those who qualify, we compare their debt-to-income (DTI) ratio. A lower DTI ratio indicates a more favorable financial position relative to their income. The DTI ratio is calculated by dividing monthly recurring debt by monthly gross income, where monthly gross income is the annual income divided by \(12\).
- Down Payment Eligibility Check
For each person, we calculate the required down payment (\(0.20 \times \text{home value}\)) and compare it to their savings:
- Person A: Required down payment is \(0.20 \times \$175,000 = \$35,000\). Savings: \(\$35,000\). Eligible: Yes (\(\$35,000 \ge \$35,000\)).
- Person B: Required down payment is \(0.20 \times \$200,000 = \$40,000\). Savings: \(\$40,000\). Eligible: Yes (\(\$40,000 \ge \$40,000\)).
- Person C: Required down payment is \(0.20 \times \$220,000 = \$44,000\). Savings: \(\$42,000\). Eligible: No (\(\$42,000 < \$44,000\)).
- Person D: Required down payment is \(0.20 \times \$250,000 = \$50,000\). Savings: \(\$50,000\). Eligible: Yes (\(\$50,000 \ge \$50,000\)).
Person C is disqualified for not meeting the down payment requirement.
- DTI Ratio Comparison and Final Evaluation
Now we calculate the DTI ratio for the eligible candidates (A, B, and D). Monthly income is annual income divided by \(12\), and the DTI is \(\frac{\text{monthly recurring debt}}{\text{monthly income}}\):
- Person A: Monthly income = \(\frac{\$51,000}{12} = \$4,250\). DTI = \(\frac{\$350}{\$4,250} \approx 0.0824\).
- Person B: Monthly income = \(\frac{\$58,000}{12} = \$4,833.33\). DTI = \(\frac{\$250}{\$4,833.33} \approx 0.0517\).
- Person D: Monthly income = \(\frac{\$67,000}{12} = \$5,583.33\). DTI = \(\frac{\$450}{\$5,583.33} \approx 0.0806\).
Comparing these values, Person B has the lowest DTI ratio (\(\approx 0.0517\)).
- Conclusion
Based on the analysis, Person B meets the \(20\%\) down payment requirement and holds the lowest debt-to-income ratio among the eligible candidates, making them the most qualified applicant for the home loan. The final answer is \(\boxed{b}\).
Examples
In the world of finance, mortgage lenders use these metrics to assess the risk of a potential borrower. By calculating down payment requirements and debt-to-income ratios, lenders can ensure they lend money to individuals who are financially responsible and capable of making long-term mortgage payments. Understanding these calculations helps individuals prepare their own finances for major purchases like homes, ensuring they reach their goals efficiently and successfully.