A property is valued at $800,000 with a first mortgage of $600,000. What is the loan-to-value ratio?
Correct Answer
A) 75%
Loan-to-value ratio is calculated by dividing the loan amount by the property value: $600,000 ÷ $800,000 = 0.75 or 75%.
Why This Is the Correct Answer
Option A (75%) is correct because the LTV ratio is calculated by dividing the loan amount by the property value and converting to a percentage. Using the formula: $600,000 (loan) ÷ $800,000 (property value) = 0.75. When converted to a percentage, 0.75 equals 75%. This means the borrower is financing 75% of the property's value and has 25% equity.
Why the Other Options Are Wrong
Option B: 80%
Option B (80%) is incorrect because it represents a miscalculation of the LTV ratio. This percentage would result from dividing $640,000 by $800,000, not the actual loan amount of $600,000. Students might arrive at this answer through computational errors or confusion with common LTV thresholds.
Option C: 25%
Option C (25%) is incorrect because it represents the equity percentage, not the loan-to-value ratio. This is calculated as ($800,000 - $600,000) ÷ $800,000 = 25%, which shows how much of the property value the owner has paid off, but the question specifically asks for the LTV ratio.
Option D: 133%
Option D (133%) is incorrect and results from inverting the LTV formula by dividing the property value by the loan amount ($800,000 ÷ $600,000 = 1.33 or 133%). This fundamental error in formula application would indicate the loan exceeds the property value, which doesn't make sense in this context.
LTV = Loan Takes Value
Remember 'LTV = Loan Takes Value' - the Loan amount 'Takes' a percentage of the total Value. Always put the smaller number (loan) on top and the larger number (property value) on the bottom: Loan ÷ Value = LTV%.
How to use: When you see an LTV question, immediately identify the loan amount and property value, then remember 'Loan Takes Value' to put loan amount in the numerator and property value in the denominator.
Exam Tip
Always double-check that your LTV percentage is less than 100% in normal lending scenarios - if you get over 100%, you've likely inverted the formula.
Common Mistakes to Avoid
- -Inverting the formula by putting property value over loan amount
- -Calculating equity percentage instead of LTV ratio
- -Forgetting to convert the decimal to a percentage
Concept Deep Dive
Analysis
The loan-to-value (LTV) ratio is a fundamental financial metric used in real estate lending and appraisal that measures the relationship between the loan amount and the appraised value of the property. This ratio is expressed as a percentage and helps lenders assess the risk level of a mortgage loan. A lower LTV ratio indicates less risk for the lender because the borrower has more equity in the property. LTV ratios are crucial for determining loan approval, interest rates, and whether private mortgage insurance (PMI) is required.
Background Knowledge
Loan-to-value ratio is one of the most important risk assessment tools used by lenders to evaluate mortgage applications. The formula is always: Loan Amount ÷ Property Value × 100 = LTV%. Most conventional loans require LTV ratios of 80% or less to avoid private mortgage insurance requirements.
Real-World Application
Appraisers must understand LTV ratios because lenders use these calculations to determine loan approval and terms. If an appraisal comes in lower than expected, it can increase the LTV ratio and potentially require the borrower to make a larger down payment or pay for mortgage insurance.
More Math & Stats Questions
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