Question

The Ohio Valley Steel Corporation has borrowed $4.5 million for one month at a stated annual rate of 8.1%​, using inventory stored in a field warehouse as collateral. The warehouser charges a $5,750 ​fee, payable at the end of the month. What is the effective annual rate of this​ loan?

Answer 1

The monthly interest rate is 8.1%/12 = 0.675%, so Ohio Valley Steel must pay 0.0675 x $4,500,000 = $30,375 in interest on the loan.

Combining this the $5,750 warehouse fee makes the monthly cost of the loan $36,125.

Since the fee is paid at the end of the month, Ohio Valley Steel has use of the full $4,500,000 for the month. The interest rate per period is $36,125 / $4,500,000 = 0.8028%. there are 12 months in a year, so the effective annual rate is (1.008028)^12–1 = 10.0703%