A borrower obtains a $300,000 mortgage at 4% annual interest, compounded semi-annually, with a 25-year amortization. What is the approximate monthly payment?

Q: What is the correct answer to: A borrower obtains a $300,000 mortgage at 4% annual interest, compounded semi-annually, with a 25-year amortization. What is the approximate monthly payment?

The correct answer is $1,582. Option B ($1,582) correctly applies the Canadian semi-annual compounding method. The 4% annual rate becomes 2% semi-annually, which converts to approximately 0.3274% monthly effective rate using the formula (1.02)^(1/6) - 1. Applying this rate to the standard payment formula with $300,000 principal over 300 months (25 years) yields approximately $1,582. This calculation method is mandated by Canadian banking regulations and differs from simple monthly compounding used in other jurisdictions.

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

Canadian mortgages are regulated under federal banking legislation requiring semi-annual interest compounding, unlike monthly compounding in other countries. The effective monthly rate calculation involves converting the semi-annual rate using compound interest principles: (1 + semi-annual rate)^(1/6) - 1. The standard mortgage payment formula then applies: M = P[r(1+r)^n]/[(1+r)^n-1], where M is monthly payment, P is principal, r is monthly effective rate, and n is total payments. This knowledge is essential for mortgage qualification, stress testing under federal guidelines, and accurate client counseling on affordability.

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

Remember SEMI: Semi-annual compounding, Effective monthly rate conversion, Monthly payment formula, Interest calculated twice yearly. Think 'Canada compounds SEMI-annually' - like a semi-truck making two stops per year at the interest station. When you see Canadian mortgage calculations, immediately think SEMI. First convert the annual rate to semi-annual, then to effective monthly rate using the compound formula, finally apply to the payment calculation.

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, then use (1 + semi-annual rate)^(1/6) - 1 for monthly rate before applying payment formula.

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

A real estate agent in Toronto helps first-time buyers understand their $300,000 mortgage options. The lender quotes 4% annually, and buyers ask about monthly payments. The agent must correctly calculate $1,582 monthly payments using semi-annual compounding to ensure accurate affordability assessment. This prevents buyers from overextending financially and ensures compliance with mortgage stress test requirements. Incorrect calculations could lead to qualification issues or client dissatisfaction when actual payments differ from expectations.

Question

Mortgage & Real Estate FinancePayment CalculationsMEDIUM

A borrower obtains a $300,000 mortgage at 4% annual interest, compounded semi-annually, with a 25-year amortization. What is the approximate monthly payment?

Answer Options

A

$1,482

B

$1,582

C

$1,682

D

$1,782