A vendor offers terms of 3/10,n/30.What is the ANNUAL interest rate the vendor is charging a buyer who does not pay within 10 days? (Assume there are 360 days in the year.

Question

Quizplus · Accepted Answer

The terms "3/10, n/30" mean that the buyer can take a 3% discount if they pay within 10 days, otherwise the full amount is due within 30 days.

To find the annual interest rate that the vendor is charging a buyer who does not pay within 10 days, we need to calculate the effective interest rate for a payment made after 10 days.

Assuming a $100 invoice, if the buyer pays within 10 days, they get a $3 discount and pay $97. If the buyer pays after 10 days, they owe the full $100.

If the buyer takes the discount, they pay $97 for the product and save $3. If they do not take the discount, they pay $100 for the product. So, the effective interest rate for not taking the discount is:

Effective interest rate = Discount / (Full payment - Discount) x (360 / (Payment days - Discount days))
Effective interest rate = 3 / (100 - 3) x (360 / (30 - 10))
Effective interest rate = 3 / 97 x 18
Effective interest rate = 0.0557 or 5.57%

Therefore, the vendor is charging an annual interest rate of 5.57% to a buyer who does not pay within 10 days.

The best choice is C, 54%, as the effective interest rate of 5.57% multiplied by the number of payment periods in a year (360/20 = 18) gives an annual interest rate of 54%.

A Vendor Offers Terms of 3/10,n/30