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 beginning of the loan. What is Matt's EAR?

The Matt's EAR is 7.24%

Explanation:

The money borrowed by the company (L) = $10 million

Time period for the loan (T) = 4 months

Rate given (APR) = 5.5%

Per Month rate R=5.5%/12=0.46%

The fee of warehouse that is paid at the starting of the loan = 0.5%

Now we have to calculate the Matt’s EAR.

Warehouse fees =0.5%

So Fees F= 0.5% × L = 0.5% × $10 = $0.05 millions

Therefore, the Net amount we get N = L – F = 10 - 0.5 = $9.95 millions

Assume  r be the per month EAR

N*(1+r)^4 = L*(1+R)^4

9.95*(1+r)^4 = 10*(1+0.46%)^4

r=0.58%

EAR =(1+r)^12-1= (1+0.58%)^12-1 = 7.24%