Let's break this down step-by-step.

Part a: Brian's actual rate of return

We can use the formula for the rate of return (ROR) based on the selling price, purchase price, and the number of days Brian held the paper:

$\text{ROR (Brian)} = \left( \frac{\text{Selling Price} - \text{Purchase Price}}{\text{Purchase Price}} \right) \times \left( \frac{365}{\text{Days Held}} \right)$

Where:

• Purchase Price = $134,010.61
• Selling Price = $135,759.45
• Days Held = 92

Now, we can calculate:

$\text{ROR (Brian)} = \left( \frac{135,759.45 - 134,010.61}{134,010.61} \right) \times \frac{365}{92}$

Part b: Jordan's actual rate of return

Jordan held the commercial paper for the remaining time, which is $180 - 92 = 88$ days. We can use the same formula as before, but now with Jordan's purchase price and the final value at maturity.

$\text{ROR (Jordan)} = \left( \frac{137,000 - 135,759.45}{135,759.45} \right) \times \frac{365}{88}$

Part c: Brian's rate of return if held until maturity

If Brian had held the paper until its maturity date, his rate of return would be based on the difference between the maturity value and the initial purchase price, over the entire 180-day period:

$\text{ROR (Brian until maturity)} = \left( \frac{137,000 - 134,010.61}{134,010.61} \right) \times \frac{365}{180}$

Let's calculate all these values.### Results:

a. Brian's actual rate of return: 5.18%

b. Jordan's actual rate of return: 3.79%

c. Brian's rate of return if held until maturity: 4.52%

Would you like further details or clarifications?

Here are 5 related questions for deeper understanding:

1. What factors affect the rate of return on short-term commercial papers?
2. How would the rates change if the paper had a different face value?
3. What are the risks involved in buying and selling commercial papers?
4. Can the rate of return be compared directly between different maturities of commercial papers?
5. How does the holding period impact the rate of return in general?

Tip: Always consider the time value of money when calculating returns, especially for short-term investments like commercial paper.