To solve the problem, let's calculate the rates of return for Tara and Kenneth based on the given information. The formulas we'll use are:

Formula for Rate of Return:

$\text{Rate of Return (R)} = \frac{\text{Profit}}{\text{Initial Investment}} \times \frac{360}{\text{Holding Period}}$

Where:

• Profit = Final Sale Price - Initial Purchase Price
• Initial Investment = Initial Purchase Price
• Holding Period is the number of days the investment was held.

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a. Tara's Actual Rate of Return

• Initial Investment: $129,090.85
• Final Sale Price: $130,809.70
• Profit:
  $\text{Profit} = 130,809.70 - 129,090.85 = 1,718.85$
• Holding Period: 93 days

Substitute into the formula: $R = \frac{1,718.85}{129,090.85} \times \frac{360}{93}$

$R = 0.013316 \times 3.87097 = 0.05155 \text{ or } 5.16\%$

Tara's actual rate of return: 5.16%

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b. Kenneth's Actual Rate of Return

• Initial Investment: $130,809.70
• Final Maturity Value: $132,000
• Profit:
  $\text{Profit} = 132,000 - 130,809.70 = 1,190.30$
• Holding Period: $180 - 93 = 87 \, \text{days}$

Substitute into the formula: $R = \frac{1,190.30}{130,809.70} \times \frac{360}{87}$

$R = 0.0091 \times 4.13793 = 0.03769 \text{ or } 3.77\%$

Kenneth's actual rate of return: 3.77%

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c. Tara's Rate of Return if Held to Maturity

If Tara had held the note until its maturity date:

• Initial Investment: $129,090.85
• Final Maturity Value: $132,000
• Profit:
  $\text{Profit} = 132,000 - 129,090.85 = 2,909.15$
• Holding Period: 180 days

Substitute into the formula: $R = \frac{2,909.15}{129,090.85} \times \frac{360}{180}$

$R = 0.02255 \times 2 = 0.0451 \text{ or } 4.51\%$

Tara's rate of return if held to maturity: 4.51%

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Final Answers:

• a. Tara's Actual Rate of Return: 5.16%
• b. Kenneth's Actual Rate of Return: 3.77%
• c. Tara's Rate of Return if Held to Maturity: 4.51%

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Would you like me to explain any step in more detail or verify the calculations? 😊

Related Questions:

1. How does the holding period affect the rate of return in these calculations?
2. Why does Tara's return change if she holds the note to maturity?
3. What other factors could influence the returns besides holding period and price?
4. How does the 360-day year assumption simplify these calculations?
5. Could these rates of return be compared to a simple interest rate on a savings account?

Tip: Always use consistent timeframes (e.g., 360-day year) when comparing financial returns across different investments.