A client has a $300,000 mortgage at 4.5% annually, compounded semi-annually, with a 25-year amortization. What is the monthly payment amount?

Q: What is the correct answer to: A client has a $300,000 mortgage at 4.5% annually, compounded semi-annually, with a 25-year amortization. What is the monthly payment amount?

The correct answer is $1,668.56. Option A ($1,668.56) is correct because it properly applies the Canadian mortgage calculation method. With semi-annual compounding at 4.5% annually, the effective semi-annual rate is 2.25%. This converts to an effective monthly rate of approximately 0.3675%. Using the payment formula PMT = PV × [r(1+r)^n]/[(1+r)^n-1] where PV=$300,000, monthly rate=0.003675, and n=300 months (25 years), the calculation yields $1,668.56. This follows standard Canadian mortgage calculation protocols used by financial institutions.

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

Canadian mortgages use semi-annual compounding as the standard, established by banking regulations and industry practice. This differs from US mortgages which typically use monthly compounding. The calculation involves converting the annual rate to an effective semi-annual rate, then to an effective monthly rate. The payment formula considers principal, interest rate, and amortization period. Real estate professionals must understand these calculations to properly advise clients on affordability and help complete financing conditions. This knowledge supports compliance with professional duties under provincial real estate legislation.

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

Remember SEMI: Semi-annual is Standard, Effective rate conversion, Monthly payment calculation, Interest compounded twice yearly. Think of Canada as 'semi-friendly' - we compound semi-annually, not monthly like our southern neighbors. When you see Canadian mortgage calculations, immediately think SEMI. First convert annual rate to semi-annual, then to effective monthly rate, then apply the payment formula. This prevents using incorrect US-style monthly compounding.

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

For Canadian mortgage payments, always convert semi-annual compounding first. Divide annual rate by 2 for semi-annual rate, convert to effective monthly rate using (1+r)^(1/6)-1, then apply standard payment formula.

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

A real estate agent is helping first-time buyers determine their maximum purchase price. The buyers qualify for a $300,000 mortgage at 4.5% with 25-year amortization. By correctly calculating the monthly payment as $1,668.56, the agent can accurately assess the buyers' debt service ratios and ensure they meet lending criteria. This precise calculation helps avoid disappointment during the financing condition period and ensures the buyers can comfortably afford their new home while meeting all regulatory requirements.

Question

Mortgage & Real Estate FinanceInterest CalculationsMEDIUM

A client has a $300,000 mortgage at 4.5% annually, compounded semi-annually, with a 25-year amortization. What is the monthly payment amount?

Answer Options

A

$1,668.56

B

$1,685.43

C

$1,702.18

D

$1,719.85