Sarah has a $400,000 mortgage at 4.5% annual interest, compounded semi-annually, with a 25-year amortization. What would be her approximate monthly payment?

Q: What is the correct answer to: Sarah has a $400,000 mortgage at 4.5% annual interest, compounded semi-annually, with a 25-year amortization. What would be her approximate monthly payment?

The correct answer is $2,224. Option B ($2,224) is correct because it properly applies the Canadian mortgage payment formula with semi-annual compounding. The calculation converts the 4.5% annual rate to a semi-annual rate of 2.25%, then determines the effective monthly rate of approximately 0.3709%. Using the payment formula P = L[c(1+c)^n]/[(1+c)^n-1] where L=$400,000, c=monthly rate, and n=300 payments (25 years × 12), the result is approximately $2,224.

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

Canadian mortgages are governed by federal banking regulations requiring semi-annual compounding of interest, unlike the monthly compounding common in other countries. The Interest Act of Canada mandates this structure. Real estate professionals must understand the payment calculation formula: P = L[c(1+c)^n]/[(1+c)^n-1], where P is payment, L is loan amount, c is effective monthly rate, and n is number of payments. The effective monthly rate is calculated as (1 + annual rate/2)^(1/6) - 1. This knowledge is essential for mortgage pre-qualification and client counseling.

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, Monthly payments, Interest Act compliance. Think of a semi-truck making deliveries twice per year (semi-annually) but customers paying monthly installments. When you see Canadian mortgage calculations, immediately think SEMI to remember the semi-annual compounding requirement. This triggers the correct formula sequence: annual rate → semi-annual → effective monthly → payment calculation.

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

For Canadian mortgage payments, always convert semi-annual compounding to effective monthly rate first. Quick check: monthly payment should be roughly 0.55-0.60% of loan amount for typical rates and 25-year amortization.

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

A real estate agent is working with first-time buyers Sarah and John who are pre-approved for $400,000. They want to know their exact monthly payment to budget properly. The agent must accurately calculate $2,224 using the semi-annual compounding method to ensure the clients can afford the home and avoid payment shock. Providing the wrong calculation could lead to financial hardship or lost sales if buyers are misinformed about their true obligations.

Question

Mortgage & Real Estate FinancePayment CalculationsMEDIUM

Sarah has a $400,000 mortgage at 4.5% annual interest, compounded semi-annually, with a 25-year amortization. What would be her approximate monthly payment?

Answer Options

A

$2,108

B

$2,224

C

$2,340

D

$2,456