A borrower has a $400,000 mortgage at 5% annual interest, compounded semi-annually, amortized over 25 years. What is the approximate monthly payment?
Correct Answer
B) $2,326
Converting 5% compounded semi-annually to a monthly rate gives (1 + 0.05/2)^(1/6) - 1 = 0.41239%. Applying the payment formula to $400,000 over 300 monthly payments gives $400,000 x 0.0041239 / (1 - 1.0041239^-300) = $2,326.42, or about $2,326. Using 5%/12 as the monthly rate would wrongly assume monthly compounding and give about $2,338.
Why This Is the Correct Answer
This is correct because the equivalent monthly rate for 5% compounded semi-annually is 0.41239%, and applying the payment formula to $400,000 over 300 months produces $2,326.42, which rounds to $2,326.
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A borrower has a $400,000 mortgage at 5% annual interest, amortized over 25 years. If they make an additional principal payment of $10,000, what is the primary benefit?
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