d'Anconia Copper has borrowed $5 million for six months at a stated annual rate of 10%,using inventory stored in a field warehouse as collateral.The warehouse charges a $25,000 fee,payable at the end of the six months.The effective annual rate on this loan is closest to:

Question

Quizplus · Accepted Answer

First, we need to calculate the interest on the loan:
Interest = $5 million x 10% x 6/12 = $250,000

Next, we need to add the warehouse fee to the total cost of the loan:
Total Cost = Interest + Warehouse Fee = $250,000 + $25,000 = $275,000

To calculate the effective annual rate (EAR), we use the following formula:

EAR = (1 + Stated Rate / m)^m - 1
where m is the number of compounding periods per year

In this case, m = 2 since the loan is for six months. Plugging in the numbers, we get:

EAR = (1 + 0.10 / 2)^2 - 1 = 0.1051 or 10.51%

However, we need to factor in the warehouse fee in the calculation of EAR. One way to do this is to treat the fee as a loan origination fee and add it to the principal:

Principal = $5 million + $25,000 = $5,025,000

Using the same formula as before, we get:

EAR = (1 + 0.10 / 2)^2 - 1 = 0.1131 or 11.31%

Therefore, the closest answer choice is B) 11.3%.

D'Anconia Copper Has Borrowed $5 Million for Six Months at a Stated