Question

A store will give you a 2.50% discount on the cost of your purchase if you pay cash today. otherwise, you will be billed the full price with payment due in 1 month. what is the implicit borrowing rate being paid by customers who choose to defer payment for the month? (do not round intermediate calculations. enter your answer as a percent rounded to 2 decimal places.)

Answer 1

If the purchase price of your items would be 100 $ then the price you would have to pay immediately is 97,50 $, or 100 $ by the end the month. Compared to the 97,5 $, this is an increase of ((100/97,5)-1)*100 = 2,56410.. or 2,56 %. This is the increase to get back to $ 100. Now if these interests are compounded, it will imply that you have to pay these interests, each month on a growing amount of money. This means that we don't multiplie this percent by 12 but that it goes to the 12th power. In order to do math correctly. You need to make the monthly multiplying factor to the 12th power which is (100/97,5)^12 = 1,35501... This gives (1,35501*100)-100 or 35,50% interest on a yearly basis. Quite high if you think about it.