Questions: Hard Blues Music buys CDs with a list price of 39,000. If the wholesaler offers trade discounts of 6 / 5 / 4, find the net price factor.

Solution Steps

To find the net price factor given a series of trade discounts, we need to calculate the cumulative effect of the discounts on the list price. The net price factor is the product of the complements of each discount rate.

Given trade discounts of \(6\%\), \(5\%\), and \(4\%\), we first convert these percentages to their decimal form: \[ \text{Discounts} = [0.06, 0.05, 0.04] \]

Next, we calculate the complements of these discounts. The complement of a discount is \(1 - \text{discount}\): \[ \text{Complements} = [1 - 0.06, 1 - 0.05, 1 - 0.04] = [0.94, 0.95, 0.96] \]

The net price factor is the product of the complements of the discounts: \[ \text{Net Price Factor} = 0.94 \times 0.95 \times 0.96 \]

Performing the multiplication: \[ 0.94 \times 0.95 = 0.8930 \] \[ 0.8930 \times 0.96 = 0.85728 \]

Final Answer