A loan has an original principal of $400,000 and annual debt service of $30,400. What is its mortgage constant?
Correct Answer
B) 7.6%
The mortgage constant is the ratio of annual debt service to the loan principal: $30,400 ÷ $400,000 = 7.6%. Inverting the ratio gives 13.2, and using one month’s payment or misplacing the decimal gives the other choices.
Why This Is the Correct Answer
Option B is correct because the mortgage constant is annual debt service divided by the loan principal: $30,400 ÷ $400,000 = 0.076, or 7.6%. This ratio is also called the debt capitalization rate.
Why the Other Options Are Wrong
Option A: 13.2%
Option A, 13.2%, comes from inverting the ratio ($400,000 ÷ $30,400 = about 13.2). The mortgage constant places debt service over principal: $30,400 ÷ $400,000 = 7.6%.
Option C: 0.63%
Option C, 0.63%, uses one monthly payment ($30,400 ÷ 12 ÷ $400,000). The mortgage constant uses annual debt service: $30,400 ÷ $400,000 = 7.6%.
Option D: 76.0%
Option D, 76.0%, results from misplacing the decimal ($30,400 ÷ $400,000 × 1,000). Converting 0.076 to a percentage means multiplying by 100, giving 7.6%.
Payment over principal
Mortgage constant equals annual Payment over Principal, both measured on an annual basis.
How to use: Use it to set up the ratio correctly before dividing.
Exam Tip
Confirm the debt service is annual, not monthly, before dividing. A mortgage constant is normally somewhat higher than the loan's interest rate because it includes principal repayment, so a result in double digits like 13.2 or 76% or below 1% signals an inverted ratio, a decimal slip or a monthly figure.
Common Mistakes to Avoid
- -Dividing principal by debt service
- -Using a monthly payment instead of annual debt service
- -Misplacing the decimal when converting to a percentage
Concept Deep Dive
Analysis
This question tests the definition and calculation of the mortgage constant. The mortgage constant, also called the debt capitalization rate (RM), is annual debt service divided by the loan principal. Keep annual figures together and place debt service in the numerator.
Background Knowledge
The mortgage constant expresses the annual payment, covering both interest and principal, as a percentage of the loan amount. It is used in income capitalization techniques such as the band of investment and in analyzing debt coverage. In appraisal it is the debt capitalization rate, labeled RM.
Real-World Application
An appraiser valuing a fourplex uses typical loan terms to estimate the mortgage constant. That rate becomes the debt component in a band of investment calculation for the overall capitalization rate.
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