A firm offers credit terms of 1/5, net 15. What is the effective annual rate on the credit extended if a customer foregoes the discount on a $2,000 purchase?
A) 27.70%
B) 31.23%
C) 36.00%
D) 44.31%
E) 47.98%

Question

Quizplus · Accepted Answer

The effective annual rate (EAR) can be calculated using the formula for EAR when a discount is not taken. The terms 1/5, net 15 mean that the customer gets a 1% discount if they pay within 5 days; otherwise, the net (full) amount is due in 15 days. If the customer foregoes the discount, they are effectively borrowing the amount they could have saved for 10 days (15 days - 5 days). The discount they forego is 1% of $2,000, which is $20. So, they are paying an extra $20 on $1,980 (since they could have paid $1,980 instead of $2,000) for 10 days. To annualize this rate, we use the formula for EAR:EAR = (1 + i)^n - 1where i is the interest rate per period, and n is the number of periods per year. In this case, i = $20/$1,980 = 0.0101 (or 1.01%), and the period is 10 days. There are approximately 365/10 = 36.5 periods in a year.EAR = (1 + 0.0101)^36.5 - 1 ≈ 44.31%Therefore, the effective annual rate on the credit extended is approximately 44.31%.

A Firm Offers Credit Terms of 1/5, Net 15