A loan’s original principal is $480,000 and level monthly principal-and-interest payment is $3,000. What annual mortgage constant is twelve monthly payments ÷ original principal?
Correct Answer
B) 7.50%
3000×12÷480000×100 = 7.5. Common errors: using one monthly payment instead of twelve gives 0.63%; misplacing the decimal (×1,000 instead of ×100) gives 75.00%; inverting the ratio (principal ÷ annual payments) gives 13.33%.
Why This Is the Correct Answer
Option B is correct because annual debt service is $3,000 × 12 = $36,000. Dividing by the $480,000 principal gives 0.075, which is 7.50%.
Why the Other Options Are Wrong
Option A: 0.63%
Option A, 0.63%, comes from using one monthly payment instead of twelve: $3,000 ÷ $480,000 × 100 = 0.625, or 0.63%. The annual constant uses $36,000 of annual payments, giving 7.50%.
Option C: 13.33%
Option C, 13.33%, comes from inverting the ratio: $480,000 ÷ $36,000 = 13.33. The constant puts annual payments on top, giving $36,000 ÷ $480,000 = 7.50%.
Option D: 75.00%
Option D, 75.00%, comes from misplacing the decimal: $36,000 ÷ $480,000 × 1,000 = 75. The correct conversion is 0.075 × 100 = 7.50%.
Twelve payments over principal
Annualize the monthly payment first, then divide by the loan amount. The constant covers both interest and amortization.
How to use: Use this whenever a problem gives a monthly payment and asks for an annual mortgage constant.
Exam Tip
Check whether the payment given is monthly or annual before dividing, and do not confuse the mortgage constant with the interest rate.
Common Mistakes to Avoid
- -Using one monthly payment instead of the annual total
- -Substituting the loan interest rate for the mortgage constant
- -Dividing principal by annual payments
Concept Deep Dive
Analysis
This question tests calculation of the annual mortgage constant. It is total annual debt service divided by the original loan principal. The candidate must annualize the monthly payment before dividing.
Background Knowledge
The annual loan or mortgage constant is the ratio of annual debt service to the loan principal. It reflects both interest and principal repayment, so it exceeds the interest rate on an amortizing loan. It is used in the band of investment and the debt coverage formula.
Real-World Application
An appraiser building a band of investment learns that typical loans for the property type carry a monthly payment of $3,000 on $480,000. She computes the 7.5% annual constant to use as the mortgage component.
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Previous Question
A lender underwrites a loan at a 1.25 debt coverage ratio, a 7.5% annual mortgage constant, and a 70% loan-to-value ratio. What overall capitalization rate does the debt coverage formula indicate, rounded to one decimal place?
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Annual PGI is $360,000 and combined vacancy and collection loss is explicitly 8% of that same PGI base. There is no other income. What annual EGI remains?