A contractor's license bond costs $450 annually for $15,000 coverage. If the contractor needs to increase coverage to $25,000 due to a claim, and the rate increases proportionally, what is the new annual cost?
Correct Answer
C) $750
Rate per $1,000 = $450 ÷ 15 = $30. New cost = $30 × 25 = $750 annually for $25,000 coverage.
Why This Is the Correct Answer
Use proportional rate calculation. Rate per $1,000 of coverage = $450 ÷ 15 = $30 per $1,000. New annual cost = $30 × 25 = $750. The rate stays constant at $30 per $1,000, so scaling up to $25,000 coverage directly yields $750.
Why the Other Options Are Wrong
Option A: $850
The $850 figure does not follow proportional scaling. It appears to add a flat $400 to the original premium rather than recalculating at the correct per-$1,000 rate. This approach has no mathematical basis in the problem.
Option B: $650
The $650 figure is incorrect. It may result from miscalculating the rate (e.g., dividing $450 by 10 instead of 15) or applying incorrect arithmetic. The actual rate is $30 per $1,000, giving $750 for $25,000 coverage.
Option D: $950
The $950 figure exceeds the correct answer and may come from using an incorrect rate or adding unnecessary surcharges. With proportional scaling at $30 per $1,000, $25,000 coverage costs exactly $750.
Memory Technique
Step 1: Find rate per $1,000 (divide old premium by old coverage in thousands). Step 2: Multiply that rate by new coverage in thousands. Two steps, done.
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