A borrower has a $300,000 mortgage at 4% interest, compounded semi-annually, with a 25-year amortization. What is the approximate monthly payment?
Correct Answer
D) $1,578
Canadian fixed-rate mortgages compound semi-annually, so the monthly rate is (1 + 0.04/2)^(1/6) - 1 = 0.3306%. Applying the payment formula to $300,000 over 300 monthly payments gives $1,578.06, or about $1,578 per month. Dividing 4% by 12 (monthly compounding) would give $1,584, which overstates the Canadian payment.
Why This Is the Correct Answer
This answer is correct. The monthly rate is 1.02^(1/6) - 1 = 0.0033059. The payment is P x r / (1 - (1 + r)^-n) = 300,000 x 0.0033059 / (1 - 1.0033059^-300) = $1,578.06, or about $1,578 a month over the 25-year (300-payment) amortization.
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A borrower has a $300,000 fixed-rate mortgage at 4% per year, compounded semi-annually, with monthly payments. What effective monthly interest rate is used to calculate the payment?
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