To calculate the yield to maturity (YTM) for Abner Corporation's bond, we need to use the following information:

• Face value (FV): Bonds typically have a face value of $1,000 (if not specified otherwise).
• Coupon rate: 9% annually.
• Coupon payment: 9% of the face value, which is 9% of $1,000 = $90 per year.
• Current price (P): $1,125.
• Time to maturity (n): 17 years.

The formula for calculating the YTM involves solving the following equation:

$P = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{FV}{(1 + r)^n}$

Where:

• $P$ is the current bond price ($1,125).
• $C$ is the annual coupon payment ($90).
• $FV$ is the face value of the bond ($1,000).
• $n$ is the number of years to maturity (17 years).
• $r$ is the yield to maturity (the value we're solving for).

This equation is generally solved through numerical methods or using a financial calculator because it's difficult to solve algebraically due to the $r$ appearing in multiple terms. However, we can use an approximation method to estimate the YTM.

Approximation Formula for YTM:

A common approximation formula for YTM is:

$YTM \approx \frac{C + \frac{FV - P}{n}}{\frac{FV + P}{2}}$

Where:

• $C$ is the coupon payment ($90),
• $FV$ is the face value ($1,000),
• $P$ is the price ($1,125),
• $n$ is the years to maturity (17 years).

Step-by-step calculation:

1. Coupon Payment (C) = $90
2. Face Value (FV) = $1,000
3. Price (P) = $1,125
4. Years to Maturity (n) = 17

Using the formula:

$YTM \approx \frac{90 + \frac{1,000 - 1,125}{17}}{\frac{1,000 + 1,125}{2}}$

Now, let's compute this:

$YTM \approx \frac{90 + \frac{-125}{17}}{\frac{2,125}{2}}$ $YTM \approx \frac{90 - 7.35}{1,062.5}$ $YTM \approx \frac{82.65}{1,062.5} \approx 0.0778 \text{ or } 7.78\%$

Conclusion:

The approximate yield to maturity (YTM) for the bond is 7.78%.

Would you like more details on how to calculate YTM or use a different method? Here are some related questions that might help expand your understanding:

1. How does the YTM change if the bond is purchased at a discount or premium?
2. What is the difference between YTM and current yield?
3. How do coupon rates affect bond pricing?
4. How can a financial calculator be used to solve for YTM?
5. What is the impact of market interest rate changes on YTM?

Tip: If you have access to a financial calculator or spreadsheet software (like Excel), you can directly use the YIELD function to find the YTM, which is much faster and precise than approximation methods.