Math Problem Statement
Solution
To solve this problem, we'll analyze the given bond details and complete the table accordingly. Here's the breakdown:
Given Data:
- Par Value: 1000
- Yield Rate: 7.6% compounded semi-annually (i.e., 3.8% per period)
- Coupon Rate: 5.6% compounded semi-annually (i.e., 2.8% per period)
- Book Value after 5th Coupon: 1100
Key Concepts:
-
Coupon Payment Calculation:
- Semi-annual coupon rate = .
- Thus, each coupon payment is 28.
-
Interest Calculation:
- The semi-annual yield rate is .
- Interest earned for the 5th coupon period is calculated as:
-
Principal Adjustment:
- The principal adjustment is the difference between the book value at the end of the previous period plus the coupon payment and the book value after the current period.
Completing the Table:
Let’s fill in the details using the above calculations.
Time | Coupon | Interest | Principal | Book Value |
---|---|---|---|---|
5th Coupon | 28 | 41.8 | 30.2 | 1100 |
6th Coupon | 28 | TBD | TBD | TBD |
- For the 5th Coupon:
- Coupon: 28
- Interest: 41.8 (calculated above)
- Principal:
- Book Value: 1100 (given)
Would you like me to proceed with calculating the values for the 6th coupon or clarify any part of the current explanation?
Here are some related questions:
- How do bond yields affect the market price of bonds?
- What is the difference between the coupon rate and the yield rate?
- How do compounding frequencies impact bond valuation?
- What happens to bond prices when market interest rates change?
- How can one calculate the present value of a bond?
Tip: Understanding how semi-annual compounding works can help you better assess bond returns over different periods.
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Math Problem Analysis
Mathematical Concepts
Bond Valuation
Semi-Annual Yield
Compound Interest
Coupon Payments
Formulas
Coupon Payment = Coupon Rate × Par Value / 2
Yield Rate per Period = Annual Yield Rate / 2
Interest = Yield Rate × Book Value
Theorems
Time Value of Money
Compound Interest
Bond Pricing Adjustments
Suitable Grade Level
Grades 11-12 (or College Level Finance)
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