Math Problem Statement
(Related to Checkpoint 9.2) (Yield to maturity) Abner Corporation's bonds mature in 17 years and pay 13 percent interest annually. If you purchase the bonds for $1 comma 225, what is your yield to maturity? Question content area bottom Part 1 Your yield to maturity on the Abner bonds is
enter your response here%. (Round to two decimal places.)
Solution
To calculate the yield to maturity (YTM) for Abner Corporation's bonds, we can use the following formula for YTM approximation:
where:
- = Annual coupon payment
- = Face value of the bond (usually assumed to be $1,000 if not stated)
- = Price of the bond (purchase price)
- = Years to maturity
Given dataTo calculate the yield to maturity (YTM) for Abner Corporation's bonds, we can use the following formula for YTM approximation:
where:
- = Annual coupon payment
- = Face value of the bond (usually assumed to be $1,000 if not stated)
- = Price of the bond (purchase price)
- = Years to maturity
Given
- Coupon rate = 13% (so, annually)
- Price
- Years to maturity
- Face value (assuming this is standard if not stated otherwise)
Let's plug these values into the approximation formula to get an initial estimate. However, for precise YTM calculation, using a financial calculator or iterative method like Excel's RATE function is typical. I'll calculate the approximate YTM first.The approximate yield to maturity (YTM) for Abner Corporation's bonds is 10.50% (rounded to two decimal places).
Would you like a detailed explanation of the steps, or do you have any additional questions?
Here are some related questions that might deepen your understanding:
- How does the bond price affect the yield to maturity?
- What is the impact of time to maturity on the YTM calculation?
- How does a bond's coupon rate compare to its YTM?
- What are other methods to calculate YTM more precisely?
- How does YTM differ from the bond’s current yield?
Tip: YTM calculations typically assume that all coupon payments are reinvested at the same rate as the YTM, which may not always be practical in real-world scenarios.
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Math Problem Analysis
Mathematical Concepts
Finance
Yield to Maturity (YTM)
Bond Pricing
Formulas
YTM ≈ (C + (F - P) / n) / ((F + P) / 2)
Theorems
-
Suitable Grade Level
College or Advanced High School (Grades 11-12)
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