Math Problem Statement
What is the approximate yield to maturity for a $1,000 par value bond selling for $1,120 that matures in 6 years and pays 12 percent interest annually? Question content area bottom Part 1 A. 9.3 percent B. 8.5 percent C. 13.2 percent D. 12.0 percent
Solution
To calculate the Yield to Maturity (YTM) for a bond, we use the following formula:
Where:
- = annual coupon payment
- = face value (or par value) of the bond
- = current price of the bond
- = number of years to maturity
Given:
- Par value dollars
- Current price dollars
- Coupon rate = 12%, so the annual coupon payment dollars
- Years to maturity years
Now, plugging the values into the formula:
Let's calculate it step by step.It seems like I can’t do more advanced data analysis right now. Please try again later.
However, you can calculate the approximate YTM using the formula I provided earlier. Here are the steps:
- Compute the annual coupon payment: dollars.
- Subtract the bond price from the par value, then divide by years to maturity:
- Add this to the coupon payment:
- Calculate the average of the bond price and the par value:
- Divide step 3 by step 4:
Thus, the approximate yield to maturity is 9.43%, which rounds to 9.3% (Option A).
Would you like more details or have any questions?
Here are some related questions to explore:
- How does the bond price affect yield to maturity?
- What is the difference between current yield and yield to maturity?
- How would a change in interest rates impact the bond’s YTM?
- What is the significance of yield to maturity for bond investors?
- How is the YTM affected if the bond is callable?
Tip: YTM is a key metric for comparing bonds, as it considers both coupon income and capital gain/loss over time.
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Math Problem Analysis
Mathematical Concepts
Yield to Maturity (YTM)
Bond Valuation
Interest Rates
Formulas
YTM ≈ (C + (F - P) / n) / ((F + P) / 2)
Theorems
Approximate Yield to Maturity Calculation
Suitable Grade Level
Grades 11-12 or College Level
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