Sarah has a $400,000 mortgage at 4.5% annual interest, compounded semi-annually, with a 25-year amortization. What is her monthly payment, to the nearest dollar?
Correct Answer
C) $2,214
With semi-annual compounding the monthly rate is (1 + 0.045/2)^(1/6) - 1 = 0.37153%. Over 300 payments, $400,000 x 0.0037153 / (1 - 1.0037153^-300) = $2,213.89, or $2,214 a month.
Why This Is the Correct Answer
Monthly rate j = 1.0225^(1/6) - 1 = 0.0037153. Payment = 400,000 x 0.0037153 / (1 - 1.0037153^-300) = $2,213.89, which rounds to $2,214.
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