Math Problem Statement
A town wants to build a park for $1 comma 200 comma 000 and issues 600 bonds for $2 comma 000 each, with a term of 7 years and a coupon rate of 6%. Consider the purchase of one such bond. Helpful video.opens in a new tab (a) What is the total return of this investment? (b) What is the average rate of return? Question content area bottom Part 1 (a) The total return is $ enter your response here. (Simplify your answer.) (b) The average rate of return is enter your response here%. (Simplify your answer. Round to two decimal places as needed.)
Solution
To solve this problem, we’ll calculate both the total return and the average rate of return for one bond.
Step 1: Total Return
- Bond Price: Each bond costs $2,000.
- Coupon Rate: 6% annually.
- The annual interest earned = .
- Term: 7 years.
- Total interest earned over 7 years = .
- Face Value: Assume the bond is redeemed at its face value of $2,000.
- Total return = .
The total return is $2,840.
Step 2: Average Rate of Return
The average rate of return can be calculated using the formula:
- Initial Investment = $2,000.
- Total Return = $2,840.
- Number of Years = 7.
The average rate of return is 6.00%.
Final Answers:
(a) The total return is $2,840.
(b) The average rate of return is 6.00%.
Would you like detailed explanations of the calculations or further help?
Here are 5 related questions to explore:
- What happens to the total return if the coupon rate is increased to 8%?
- How does the average rate of return compare for a 10-year bond with the same coupon rate?
- What would the total return be if the bond is sold at a discount (e.g., $1,800 face value)?
- How is the coupon rate determined in bond pricing?
- What is the present value of the bond's future cash flows at a 5% discount rate?
Tip: Understanding bond terms like face value, coupon rate, and maturity is key to evaluating investments effectively.
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Math Problem Analysis
Mathematical Concepts
Bond Valuation
Simple Interest
Rates of Return
Formulas
Total Interest = Bond Price × Coupon Rate × Term
Total Return = Total Interest + Face Value
Average Rate of Return = ((Total Return - Initial Investment) / (Initial Investment × Term)) × 100
Theorems
Principles of Simple Interest
Rate of Return Calculations
Suitable Grade Level
Grades 10-12
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