- Calculate the required down payment (\(15\%\) of home value) and verify if savings meet this requirement.
- Identify that Person B is ineligible due to insufficient savings.
- Calculate the monthly income and Debt-to-Income (DTI) ratio for eligible candidates (A, C, and D).
- Compare the DTI ratios to find the lowest; Person C has the lowest ratio at \(\approx 5.48\%\), making them the most eligible candidate. \(\boxed{\text{c}}\).
Explanation
- Analysis of Eligibility Criteria
To determine which person is the most eligible for a home loan, we must first assess two criteria for each applicant:
- Down Payment Requirement: The applicant must have savings of at least 15% of the home value.
- Debt-to-Income (DTI) Ratio: This is the ratio of recurring monthly debt to gross monthly income. A lower DTI ratio indicates a better ability to handle the mortgage payments and is therefore more favorable for loan eligibility.
We are provided with the following data for four individuals:
- Person A: Home value \(\$95,000\), annual income \(\$46,000\), savings \(\$20,000\), recurring debt \(\$310\).
- Person B: Home value \(\$107,000\), annual income \(\$53,000\), savings \(\$13,910\), recurring debt \(\$198\).
- Person C: Home value \(\$120,000\), annual income \(\$58,000\), savings \(\$18,000\), recurring debt \(\$265\).
- Person D: Home value \(\$128,000\), annual income \(\$60,000\), savings \(\$19,200\), recurring debt \(\$400\).
- Evaluating Savings Requirements
First, we calculate the required 15% down payment (\(0.15 \times \text{home value}\)) for each person and compare it to their available savings:
- Person A: Required down payment = \(0.15 \times \$95,000 = \$14,250\). Since \(\$20,000 \geq \$14,250\), Person A is eligible.
- Person B: Required down payment = \(0.15 \times \$107,000 = \$16,050\). Since \(\$13,910 < \$16,050\), Person B is not eligible.
- Person C: Required down payment = \(0.15 \times \$120,000 = \$18,000\). Since \(\$18,000 \geq \$18,000\), Person C is eligible.
- Person D: Required down payment = \(0.15 \times \$128,000 = \$19,200\). Since \(\$19,200 \geq \$19,200\), Person D is eligible.
Person B is disqualified due to insufficient savings.
- Calculating and Comparing DTI Ratios
Next, for the eligible candidates (A, C, and D), we calculate the monthly gross income and the DTI ratio. Monthly gross income is the annual income divided by 12, and the DTI ratio is \(\frac{\text{recurring debt}}{\text{monthly gross income}}\):
- Person A:
- Monthly income = \(\frac{\$46,000}{12} \approx \$3,833.33\)
- DTI = \(\frac{\$310}{\$3,833.33} \approx 0.0809\) or \(8.09\%\)
- Person C:
- Monthly income = \(\frac{\$58,000}{12} \approx \$4,833.33\)
- DTI = \(\frac{\$265}{\$4,833.33} \approx 0.0548\) or \(5.48\%\)
- Person D:
- Monthly income = \(\frac{\$60,000}{12} = \$5,000\)
- DTI = \(\frac{\$400}{\$5,000} = 0.0800\) or \(8.00\%\)
Comparing the DTI ratios of eligible candidates, Person C has the lowest DTI ratio (\(5.48\%\)), followed by Person D (\(8.00\%\)) and Person A (\(8.09\%\)). Thus, Person C is the most eligible.
- Conclusion
Comparing the eligibility of the candidates, we find that Person C has sufficient savings for the required 15% down payment and possesses the lowest debt-to-income ratio among all eligible individuals. Therefore, Person C is the highest-rated candidate for the home loan. The correct answer is c. \(\boxed{\text{c}}\).
Examples
The Debt-to-Income (DTI) ratio is a standard metric used by financial institutions to gauge the risk of lending money. When you apply for a mortgage, lenders calculate your DTI to determine if you can afford monthly repayments without significant financial strain. A person with a lower DTI is viewed as a safer borrower because they have more disposable income relative to their existing debt, helping them maintain stability even if unexpected expenses arise. Balancing savings for a down payment with a manageable debt load is the foundation of healthy personal finance planning.