A $112,000, 90-day commercial paper certificate issued by Bell Canada Enterprises was sold on its issue date for $110,100.
What annual rate of return will it yield to the buyer? (Use 365 days a year. Do not round your intermediate calculations. Round your final answer to three decimal places.)
Well, it seems like Bell Canada Enterprises is really clowning around with their commercial paper certificate!
To calculate the annual rate of return, we need to determine the discount on the certificate. The discount is the difference between the face value ($112,000) and the selling price ($110,100), which is $1,900.
Now, we need to calculate the discount yield. The discount yield is the discount divided by the face value, multiplied by 365 (days), divided by the number of days until maturity (90 days).
Discount Yield = (Discount / Face Value) * (365 / Number of Days until Maturity)
Let's plug in the numbers:
Discount Yield = ($1,900 / $112,000) * (365 / 90)
Calculating that out gives us:
Discount Yield = 0.016964
To convert this to a percentage, we multiply by 100:
Discount Yield = 1.6964%
So, the annual rate of return for the buyer will be approximately 1.696%.
Remember, investing in commercial paper can be quite the circus act, so always do your due diligence!
To find the annual rate of return, we need to calculate the discount rate and then convert it to an annual rate. Here's how you can do that:
Step 1: Calculate the discount amount:
Discount = Face value - Selling price
Discount = $112,000 - $110,100
Discount = $1,900
Step 2: Calculate the discount rate:
Discount Rate = (Discount / Face value) * (365 / Days to Maturity)
Discount Rate = ($1,900 / $112,000) * (365 / 90)
Discount Rate = 0.017857 * 4.055555
Discount Rate = 0.072291
Step 3: Calculate the annual rate of return:
Annual Rate of Return = (1 - Discount Rate) * (365 / Days to Maturity)
Annual Rate of Return = (1 - 0.072291) * (365 / 90)
Annual Rate of Return = 0.927709 * 4.055555
Annual Rate of Return ≈ 3.763 (rounded to three decimal places)
Therefore, the annual rate of return for the buyer of the commercial paper certificate is approximately 3.763%.
To calculate the annual rate of return, we need to use the formula for calculating yield or discount rate. The formula is:
Annual rate of return = (Discount/Purchase Price) x (365/Number of Days)
In this case, the discount is the difference between the face value and the purchase price, which is $112,000 - $110,100 = $1,900.
The purchase price is $110,100, and the number of days is 90.
Substituting these values into the formula, we can calculate the annual rate of return:
Annual rate of return = ($1,900/$110,100) x (365/90)
Calculating this expression, we have:
Annual rate of return = (0.017241) x (4.055556)
Simplifying further, we get:
Annual rate of return = 0.070043
Rounding the final answer to three decimal places, the annual rate of return will be approximately 0.070 or 7.0%.