Brian bought a $137,000, 180-day, commercial paper for $134,010.61. He sold it to Jordan 92 days later for $135,759.45, who held the paper until its maturity date. Answer the following questions.
Give your answers as a percent accurate to two decimal places.
a. What is Brian's actual rate of return?
Rate of Return: 
 %
b. What is Jordan's actual rate of return?
Rate of Return: 
 %
c. What rate of return would Brian have realized if he had held the note until its maturity date?
Rate of Return: 
 

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.

Brian bought a $137,000, 180-day, commercial paper for $134,010.61. He sold it to Jordan 92 days later for $135,759.45, who held the paper until its maturity date. Answer the following questions. Give your answers as a percent accurate to two decimal places. a. What is Brian's actual rate of return? b. What is Jordan's actual rate of return? c. What rate of return would Brian have realized if he had held the note until its maturity date?

Learn how to calculate the rate of return on a commercial paper transaction with detailed solutions for both Brian and Jordan. This example explores real-world financial mathematics, including rates of return for short-term investments and simple interest calculations. Suitable for advanced high school or college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation