McGrath Corporation recently issued 180-day commercial paper with a face value of $1,500,000 and a simple interest rate of 13 percent. The company paid a transaction fee equal to 0.3 percent of the amount issued, which was taken out of the issue amount before the company received any funds. Assuming there are 360 days in a year, what are the commercial paper's annual percentage rate (APR) and effective annual rate (rEAR), respectively?

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The APR is calculated by taking the total interest paid, adding any fees, and then dividing by the loan amount, and finally adjusting for a full year. The effective annual rate (rEAR) accounts for compounding within the year. For the McGrath Corporation, the interest is $1,500,000 \times 0.13 \times \frac{180}{360} = 97,500$. The transaction fee is $1,500,000 \times 0.003 = 4,500$. The total cost is $97,500 + 4,500 = 102,000$. The net amount received by the company is $1,500,000 - 4,500 = 1,495,500$. The APR is calculated as $\frac{102,000}{1,495,500} \times \frac{360}{180} = 0.1459$ or 14.59%. To find the rEAR, we use the formula $1 + rEAR = (1 + \frac{APR}{n})^n$, where $n$ is the number of compounding periods per year. Since the commercial paper does not compound (it's a simple interest product), the rEAR is calculated as if it were compounded semi-annually, leading to $rEAR = (1 + 0.1459/2)^2 - 1 = 0.1512$ or 15.12%.

McGrath Corporation Recently Issued 180-Day Commercial Paper with a Face