A contractor needs 15,000 board feet of lumber. The supplier quotes $4.25 per board foot with a 5% discount for orders over 10,000 board feet and 2% additional discount for payment within 10 days. What is the total cost if both discounts apply?
Correct Answer
B) $59,456.25
Base cost: 15,000 × $4.25 = $63,750. After 5% discount: $63,750 × 0.95 = $60,562.50. After additional 2% discount: $60,562.50 × 0.98 = $59,456.25.
Why This Is the Correct Answer
The correct answer applies both discounts sequentially to the base cost. First, the 5% volume discount is applied to the original amount, then the 2% early payment discount is applied to the already-discounted amount. This compound discount calculation results in a total cost of $59,456.25, which represents the maximum savings available to the contractor.
Why the Other Options Are Wrong
Option A: $60,562.50
This amount represents the cost after only applying the first 5% volume discount ($60,562.50) but fails to apply the additional 2% early payment discount that the contractor qualifies for.
Option C: $63,750.00
This is the base cost before any discounts are applied ($63,750), ignoring both the 5% volume discount and the 2% early payment discount that the contractor qualifies for.
Option D: $58,537.50
This amount appears to incorrectly calculate the discounts, possibly by adding the percentages together (7%) rather than applying them sequentially, or by making an arithmetic error in the calculation process.
Memory Technique
Remember 'Sequential Savings' - discounts stack on top of each other, so always multiply by the remaining percentage (95% then 98%) rather than subtracting the full percentages from 100%.
Reference Hint
Florida Building Construction Standards and Practices - Chapter on Cost Estimation and Material Calculations, or Business and Finance section covering discount calculations
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