Yesterday,Smiley Company sold $22,500 of merchandise on credit.The invoice was sent today with the terms,3/10 net 40.This customer normally pays on the net date.What is the effective rate of interest the customer is paying by not taking the discount? Assume a 365-day year.

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The effective rate of interest for not taking the discount can be calculated using the formula for the cost of not taking a trade discount: $$ \text{Interest Rate} = \left( \frac{\text{Discount \%}}{100\% - \text{Discount \%}} \right) \times \left( \frac{365}{\text{Net period} - \text{Discount period}} \right) $$ Given the terms 3/10 net 40, the discount is 3%, the discount period is 10 days, and the net period is 40 days. Plugging these values into the formula gives: $$ \text{Interest Rate} = \left( \frac{3\%}{100\% - 3\%} \right) \times \left( \frac{365}{40 - 10} \right) = \left( \frac{3}{97} \right) \times \left( \frac{365}{30} \right) $$ This calculation results in an interest rate of approximately 44.86%, indicating that by not taking the discount, the customer is effectively paying an annual interest rate of 44.86%.

Yesterday,Smiley Company Sold $22,500 of Merchandise on Credit