A borrower has a $400,000 fixed-rate mortgage at 5.5% per year, compounded semi-annually, with a 25-year amortization and monthly payments. What is the approximate monthly payment?
Correct Answer
A) $2,442
The effective monthly rate is (1 + 0.055/2)^(1/6) − 1 = 0.4532%. Over 300 payments, PMT = $400,000 × 0.004532 ÷ (1 − 1.004532^−300) = $2,441.57, about $2,442. Using 5.5% ÷ 12 instead would give $2,456, which is the monthly-compounding figure.
Why This Is the Correct Answer
Using i = (1.0275)^(1/6) − 1 = 0.004532 and n = 300, the payment is 400,000 × 0.004532 ÷ (1 − 1.004532^−300) = $2,441.57, which rounds to $2,442.
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A borrower has a $400,000 mortgage at 5.5% annual interest, compounded semi-annually, with a 25-year amortization. What is the effective annual interest rate?
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