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Difficulty: Very hardWages, Salaries, and Commissions

A specialized equipment technician earns a base wage of 28.00perhourforastandard40−hourworkweek,withanyadditionalhourspaidattime−and−a−half.Thetechnicianalsoearnsatieredcommissiononequipmentsold:428.00 per hour for a standard 40-hour workweek, with any additional hours paid at time-and-a-half. The technician also earns a tiered commission on equipment sold: 4% on the first 10,000 of sales, and a higher commission rate on all sales beyond $10,000.

Last week, the technician worked 48 hours, sold 30,000worthofequipment,andhadtotalgrossearningsof30,000 worth of equipment, and had total gross earnings of 3,056.

Calculate the commission rate for the sales exceeding $10,000.

Answer:The commission rate on sales exceeding $10,000 is 【6】%.

Answer

The commission rate on sales exceeding $10,000 is 6%.
The correct answer is found by first isolating the total commission earned (3,056gross−3,056 gross - 1,456 wages = 1,600commission).Then,subtractthe1,600 commission). Then, subtract the 400 earned from the first 10,000tier.Thisleaves10,000 tier. This leaves 1,200 in commission earned on the remaining 20,000insales.Dividing20,000 in sales. Dividing 1,200 by $20,000 yields a 0.06 or 6% commission rate.

Step-by-Step Solution

1
Calculate the base pay for standard hours.
$1,120
The first 40 hours are paid at the standard rate: 40 hours × $28.00/hour.
2
Calculate the overtime pay.
$336
The overtime rate is 28.00×1.5=28.00 × 1.5 = 42.00/hour. The technician worked 8 overtime hours (48 - 40). 42.00×8=42.00 × 8 = 336.
3
Calculate the total hourly wages.
$1,456
Add the base pay and overtime pay: 1,120+1,120 + 336 = $1,456.
4
Calculate the total commission earned.
$1,600
Subtract the total hourly wages from the total gross earnings: 3,056−3,056 - 1,456 = $1,600.
5
Calculate the tier 1 commission amount.
$400
The commission is 4% on the first 10,000ofsales:10,000 of sales: 10,000 × 0.04 = $400.
6
Calculate the tier 2 commission amount and tier 2 sales volume.
Tier 2 Commission: 1,200.Tier2Sales:1,200. Tier 2 Sales: 20,000.
Subtract tier 1 commission from total commission (1,600−1,600 - 400 = 1,200).Subtracttier1salesfromtotalsales(1,200). Subtract tier 1 sales from total sales ( 30,000 - 10,000=10,000 = 20,000).
7
Determine the tier 2 commission rate.
6%
Divide the tier 2 commission by the tier 2 sales volume: 1,200÷1,200 ÷ 20,000 = 0.06, which is 6%.

Key Concept

Reverse engineering multi-tier compensation structures involving overtime wages and graduated commission rates.
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Topics

Wages, Salaries, and Commissions

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