A merchant receives an invoice for a motor boat for $20 000 with terms 4/30, n/100. What is the highest simple interest rate at which he can afford to borrow money in order to take advantage of the discount?

Suppose the merchant will take advantage of the cash discount of 4% of $20 000 = $800 by paying the bill within 30 days from the date of invoice. He needs to borrow $20 000 = $800 = $19 200. He would borrow this money on day 30 and repay it on day 100 (the day the original invoice is due) resulting in a 70-day loan. The interest he should be willing to pay on borrowed money should not exceed the cash discount $800.

r=I/pt=21.73%

The highest simple interest rate at which the merchant can afford to borrow money is 21.73%. This is a break-even rate. If he can borrow money, say at a rate of 15%, he should do so. He would borrow $19 200 for 70 days at 15%. Maturity value of the loan is $19 200(1+0.15(70/365))=$19 752.33

savings would be $20 000 ? $19 752.33 = $247.67