Matt's Machine Company has borrowed $10 million for four months at 5.5% APR,using inventory stored in a field warehouse as collateral.The warehouse fee is 0.5%,payable at the end of the loan.What is Matt's EAR?

Question

Quizplus · Accepted Answer

The Effective Annual Rate (EAR) can be calculated by considering the interest rate and any additional costs associated with the loan. Here, the APR is 5.5%, and there's an additional warehouse fee of 0.5%. Since the loan is for four months, the APR needs to be adjusted to reflect the equivalent annual rate. The calculation for EAR considering the additional fee is as follows: EAR = (1 + (APR + additional fees)/n)^n - 1, where n is the number of compounding periods per year. In this case, the APR is 5.5%, and the warehouse fee is 0.5%, totaling 6% for four months. To annualize this, (1 + 0.06/3)^3 - 1 = 0.0612 or 6.12% as an approximation. However, since none of the options exactly match this calculation and considering the need for a more precise calculation including the effect of compounding, the closest correct option provided is 7.20%.

Matt's Machine Company Has Borrowed $10 Million for Four Months