Violet Pty Ltd usually takes 50 days to pay its suppliers. In order to encourage prompt payment, supplier T offers Violet Pty Ltd a 2% discount for payment within 10 days. What is the annual percentage cost of the discount to Violet Pty Ltd?

Question

Quizplus · Accepted Answer

If Violet Pty Ltd takes the discount, they will pay 98% of the invoice amount. 
Assume the invoice amount is $100. If they pay within 10 days, they get a 2% discount, which is $2. 
So, they will pay $98 instead of $100. 
If they don't take the discount, they will pay the full amount of $100 within 50 days.

The difference in time is 40 days (50-10) and this is how much earlier they need to pay to take advantage of the discount. 
To convert this into an annual percentage cost, we can use the following formula:

Annual percentage cost = (discount percentage / (100% - discount percentage)) x (365 / Difference in days)

Annual percentage cost = (2% / (100% - 2%)) x (365 / 40)

Annual percentage cost = 0.04146 x 9.125

Annual percentage cost = 0.3784 or 37.84%

Therefore, the discount costs Violet Pty Ltd 18.92% per annum (half of 37.84%). The correct answer is D.

Violet Pty Ltd Usually Takes 50 Days to Pay Its