A borrower has a $300,000 mortgage at 5% annual interest, compounded semi-annually, amortized over 25 years. What is their approximate monthly payment?
Correct Answer
A) $1,744
With semi-annual compounding, the monthly rate is (1 + 0.05/2)^(1/6) - 1 = 0.41239%. Over 300 payments, the payment is $300,000 x 0.0041239 / (1 - 1.0041239^-300) = $1,744.81, or about $1,744. Treating the rate as 5%/12 per month (monthly compounding) would give about $1,753.77, which is not the Canadian convention for fixed-rate mortgages.
Why This Is the Correct Answer
This is correct because converting 5% compounded semi-annually to a monthly rate gives 0.41239%, and applying the payment formula over 300 months to $300,000 produces $1,744.81 per month, which rounds to $1,744.
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