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?

Q: What is the correct answer to: 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?

The correct answer is 5.58%. 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.

Q: What background knowledge is needed for this Mortgage & Real Estate Finance question?

Effective annual interest rate represents the true annual cost of borrowing when compounding is considered. In Canada, mortgage interest is typically compounded semi-annually, meaning interest is calculated and added to the principal twice per year. This differs from the nominal or stated rate, which doesn't account for compounding frequency. The formula for effective annual rate is (1 + r/n)^n - 1, where r is the nominal rate and n is the compounding periods per year. Understanding this concept is essential for mortgage comparisons and client counseling in real estate transactions.

Q: What is a good way to remember the answer to this Mortgage & Real Estate Finance question?

Remember SEMI: Semi-annual compounding Equals More Interest. Think of it as 'semi-trucks carry more load' - semi-annual compounding carries more interest cost than the nominal rate suggests. The effective rate is always slightly higher than the nominal rate when compounding occurs. When you see mortgage interest rate questions, immediately think SEMI - check if it's asking for effective rate with semi-annual compounding. If so, the answer will be slightly higher than the nominal rate shown.

Q: What exam tip applies to this Mortgage & Real Estate Finance question?

For effective annual rate calculations with semi-annual compounding, use the formula (1 + rate/2)² - 1. The result will always be slightly higher than the nominal rate. Look for the option that's about 0.08-0.15% higher than the stated rate.

Q: How does this Mortgage & Real Estate Finance concept apply in real world practice?

A real estate agent is helping first-time buyers compare mortgage offers. Bank A offers 5.5% compounded semi-annually, while Bank B offers 5.58% compounded annually. The agent must explain that despite Bank A's lower stated rate, both mortgages have the same effective annual cost of 5.58%. This knowledge helps clients make informed decisions and builds trust through accurate financial guidance. The agent can also use this understanding to help clients budget accurately for mortgage payments.

Question

Mortgage & Real Estate FinanceInterest CalculationsBCHARD

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?

Answer Options

A

5.50%

B

5.58%

C

5.61%

D

5.75%