calculate the annualized rate of return on a 200 day commercial paper. this loan does not pay periodic interest; it is a discount security. the face value of the paper is 1,000,000 and current market value is 980,000
To calculate the annualized rate of return on a discount security like commercial paper, you need to use the formula for discount yield. The discount yield is the difference between the face value of the security and its current market value, expressed as a percentage of the face value. Here's how you can calculate it:
Step 1: Determine the discount on the commercial paper.
Discount = Face Value - Current Market Value
Discount = $1,000,000 - $980,000
Discount = $20,000
Step 2: Calculate the discount yield.
Discount Yield = Discount / Face Value
Discount Yield = $20,000 / $1,000,000
Discount Yield = 0.02 or 2%
Step 3: Annualize the discount yield.
Since the discount yield is calculated over 200 days, you need to convert it to an annual rate. Assuming there are 365 days in a year, you can use the following formula:
Annualized Discount Yield = (1 + Discount Yield)^(365/Number of Days) - 1
Annualized Discount Yield = (1 + 0.02)^(365/200) - 1
Calculating this equation, you determine that the annualized rate of return on a 200-day commercial paper is approximately 3.65%.
In summary, the annualized rate of return on the commercial paper is around 3.65%, given a face value of $1,000,000 and a current market value of $980,000.