A $240,000 loan at 5% closes September 22. For this exercise, prepaid interest uses a 360-day year and includes September 22 through September 30. What is due, rounding only the final total to cents?
Correct Answer
B) $300.00: nine days using the unrounded daily interest
B. The specified nine-day period costs $300.00. Annual interest is $240,000 × 0.05 = $12,000; the unrounded daily amount is $12,000 ÷ 360. September 22–30 inclusive is nine days. $12,000 ÷ 360 × 9 = $300.00. Scope and exceptions: The 360-day convention and inclusive dates are supplied assumptions, not a universal closing rule. Rounding $33.333… to $33.33 before multiplying would incorrectly produce $299.97. Source: Prepaid interest overview — https://www.consumerfinance.gov/ask-cfpb/what-are-prepaid-interest-charges-en-161/
Why This Is the Correct Answer
B. The specified nine-day period costs $300.00. Annual interest is $240,000 × 0.05 = $12,000; the unrounded daily amount is $12,000 ÷ 360. September 22–30 inclusive is nine days. $12,000 ÷ 360 × 9 = $300.00. Scope and exceptions: The 360-day convention and inclusive dates are supplied assumptions, not a universal closing rule. Rounding $33.333… to $33.33 before multiplying would incorrectly produce $299.97.
Why the Other Options Are Wrong
Option A: $1,000: a full month of interest is collected at every closing
It charges thirty days rather than nine.
Option C: $266.67: eight days, excluding the closing date
It omits a day the exercise explicitly includes.
Option D: $333.33: ten days, including October 1
It adds a day outside the specified period.
Exam Tip
Count the specified days and retain precision until the final amount.
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