A borrower has a $400,000 mortgage at 5.5% annual interest, compounded semi-annually, with a 25-year amortization. What is the effective annual interest rate?
Correct Answer
B) 5.58%
The effective annual rate for semi-annual compounding is calculated as (1 + 0.055/2)² - 1 = 0.0558 or 5.58%. This accounts for the compounding effect and represents the true annual cost of borrowing.
Why This Is the Correct Answer
Option B (5.58%) is correct because it properly calculates the effective annual rate using the formula (1 + r/n)^n - 1, where r is the nominal rate (0.055) and n is the compounding frequency (2 for semi-annual). The calculation is (1 + 0.055/2)² - 1 = (1.0275)² - 1 = 1.0558 - 1 = 0.0558 or 5.58%. This accounts for the compounding effect that occurs twice per year in Canadian mortgage financing.
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A borrower has a $400,000 mortgage at 5% annual interest, compounded semi-annually, amortized over 25 years. What is the approximate monthly payment?
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