Annual principal and interest debt service is $28,800 on an original mortgage principal of $360,000. What annual mortgage constant is annual debt service ÷ original principal?
Correct Answer
B) 8.0%
28800÷360000×100 = 8. Common errors: inverting the ratio (principal ÷ debt service) gives 12.5%; using a monthly payment instead of annual debt service gives 0.7%; misplacing the decimal (×1,000 instead of ×100) gives 80.0%.
Why This Is the Correct Answer
Option B is correct because $28,800 ÷ $360,000 = 0.08, which is 8.0%. The annual loan constant is the ratio of the annual loan payment to the principal amount of the loan, so annual debt service goes on top and the original principal on the bottom.
Why the Other Options Are Wrong
Option A: 0.7%
Option A, 0.7%, uses a monthly payment instead of annual debt service: $28,800 ÷ 12 = $2,400, and $2,400 ÷ $360,000 × 100 = about 0.7%. The annual constant uses the full annual debt service, $28,800 ÷ $360,000 = 8.0%.
Option C: 12.5%
Option C, 12.5%, inverts the ratio: $360,000 ÷ $28,800 = 12.5. The mortgage constant is debt service divided by principal, $28,800 ÷ $360,000 = 8.0%, not principal divided by debt service.
Option D: 80.0%
Option D, 80.0%, misplaces the decimal by multiplying by 1,000 instead of 100: $28,800 ÷ $360,000 × 1,000 = 80. The correct conversion is 0.08 × 100 = 8.0%.
Payment Over Principal
The constant is what you pay each year over what you borrowed. Annual payment on top, original loan on the bottom.
How to use: Use this phrase to set up the ratio correctly before dividing on a mortgage constant question.
Exam Tip
Check that the payment figure is annual; if a monthly payment is given, multiply by 12 before dividing by the loan amount.
Common Mistakes to Avoid
- -Dividing principal by debt service instead of debt service by principal
- -Using a monthly payment as if it were annual debt service
- -Misplacing the decimal when converting to a percentage
Concept Deep Dive
Analysis
This question tests the definition and calculation of the annual mortgage constant. The constant is annual debt service divided by the original loan principal, expressed as a percentage. Distractors come from inverting the ratio, using monthly payments or misplacing the decimal.
Background Knowledge
The mortgage constant, or annual loan constant, expresses total annual principal and interest payments as a percentage of the loan amount. It is the capitalization rate for the debt component and is used in band-of-investment and mortgage-equity analysis.
Real-World Application
An appraiser developing a band-of-investment rate obtains typical loan terms from local lenders. The appraiser calculates the annual mortgage constant from the annual debt service on a typical loan and its principal, then weights it with the equity dividend rate.
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