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

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

The correct answer is $1,584. Option C ($1,584) is correct because it properly accounts for Canadian semi-annual compounding. The calculation converts the 4% annual rate compounded semi-annually to an effective monthly rate of approximately 0.3274%, then applies the payment formula: PMT = P[r(1+r)^n]/[(1+r)^n-1] where P=$300,000, effective monthly rate, and n=300 payments (25 years × 12 months). This methodology aligns with Canadian mortgage industry standards and banking regulations.

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. Unlike US mortgages with monthly compounding, Canadian lenders quote rates as annual percentages compounded twice yearly. The effective monthly rate must be calculated using the formula: monthly rate = (1 + annual rate/2)^(1/6) - 1. This system affects payment calculations, total interest, and amortization schedules. Real estate professionals must understand this for accurate affordability assessments and client advice. The calculation impacts qualifying ratios used by lenders and affects buyers' purchasing power in the Canadian market.

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

Remember 'Canada Cuts rates in HALF twice yearly' - Canadian mortgages split the annual rate into two semi-annual periods, then convert to monthly. Think of it like cutting a pizza: first cut the year in half (semi-annual), then slice each half into 6 monthly pieces. The rate 'grows' slightly each month due to compounding, like pizza slices getting a bit thicker as you cut. When you see Canadian mortgage calculations, immediately think 'Semi-Annual Split' - convert the annual rate to semi-annual periods first, then to monthly. Don't just divide by 12. Remember the pizza analogy to avoid the simple division trap.

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

For Canadian mortgage payments, never divide the annual rate by 12. Always convert semi-annual compounding to monthly first using (1 + rate/2)^(1/6) - 1, then apply the payment formula. Look for the higher payment amount among close options.

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

A real estate agent is helping first-time buyers understand their mortgage options. The lender quotes 4% compounded semi-annually on a $300,000 mortgage with 25-year amortization. The agent must accurately calculate the $1,584 monthly payment to determine if it fits the buyers' budget and debt service ratios. Underestimating the payment could lead to qualification issues or budget shortfalls, while overestimating might unnecessarily limit their house hunting range. Accurate calculations ensure proper financial planning and realistic expectations.

Question

Mortgage & Real Estate FinancePayment CalculationsMEDIUM

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

Answer Options

A

$1,479

B

$1,548

C

$1,584

D

$1,623