Final answer:
The Effective Annual Rate (EAR) of a $30,000 par value 90-day commercial paper with a 3.5% discount yield is approximately 14.49%. This calculation accounts for the compounding effect over the year.
Step-by-step explanation:
The Effective Annual Rate (EAR) of a $30,000 par value 90-day commercial paper with a 3.5% discount yield can be calculated using the following formula for EAR:
EAR = (1 + (Discount Yield / (1 - (Discount Yield * (Days to Maturity/360)))))^(365/Days to Maturity) - 1
First, convert the discount yield to a decimal, which is 0.035. The days to maturity in this case are 90. Plugging these values into the equation:
EAR = (1 + (0.035 / (1 - (0.035 * (90/360)))))^(365/90) - 1
This simplifies to:
EAR = (1 + 0.03563565)^(365/90) - 1
EAR = 1.03563565^(4.0556) - 1
EAR ≈ 0.1449 or 14.49%
This is the annualized rate taking into account the compounding effect over the year.