A roofing contractor needs commercial auto insurance for 3 trucks valued at $85,000 total. If the premium rate is $1,200 per $10,000 of coverage, what is the annual premium for full replacement coverage?
Correct Answer
C) $10,200
Coverage needed = $85,000. Premium units = $85,000 ÷ $10,000 = 8.5 units. Premium = 8.5 × $1,200 = $10,200.
Why This Is the Correct Answer
Option C ($10,200) is correct. Full replacement coverage means insuring the entire $85,000 value. Dividing by the $10,000 unit gives 8.5 units. Multiplying 8.5 × $1,200 = $10,200. The key is recognizing that 8.5 is a valid fractional unit — you do not round up to 9 unless the problem specifies rounding.
Why the Other Options Are Wrong
Option A: $10,800
$10,800 results from rounding 8.5 units up to 9 units (9 × $1,200 = $10,800). While rounding up is sometimes required when purchasing insurance in whole units, this problem asks for the calculated annual premium at the stated rate, so fractions apply.
Option B: $12,000
$12,000 results from using 10 units ($10,000 × 10 = $100,000 coverage, which is more than needed) and calculating 10 × $1,200. This error comes from misreading the $85,000 value and defaulting to a round number.
Option D: $8,500
$8,500 appears to come from multiplying $85,000 × 0.10 (10%) or some other incorrect percentage method, ignoring the per-$10,000 rate structure entirely.
Memory Technique
Formula: (Total Value ÷ $10,000) × Rate per Unit. Write it as a fraction first: $85,000 ÷ $10,000 = 8.5 units. Then multiply: 8.5 × $1,200 = $10,200. Think of it as paying for exactly 8 and a half 'blocks' of coverage.
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