To calculate the Yield to Maturity (YTM) of the bond, we need to solve for the discount rate $r$ (or YTM), which satisfies the following bond pricing formula:

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

Where:

• $P$ is the current bond price ($1,096).
• $C$ is the semiannual coupon payment ($1,000 face value × 13% annual coupon rate / 2 = $65).
• $r$ is the semiannual yield (what we are solving for).
• $F$ is the face value ($1,000).
• $n$ is the number of semiannual periods to maturity (12 years × 2 = 24 periods).

Step-by-step:

1. Identify variables:

   • Face value ($F$) = $1,000
   • Annual coupon rate = 13%, so semiannual coupon ($C$) = 13% × 1,000 / 2 = $65
   • Price ($P$) = $1,096
   • Number of periods ($n$) = 12 years × 2 = 24 periods

2. Plug values into the bond price formula:

$1,096 = 65 \left( \frac{1 - (1 + r)^{-24}}{r} \right) + \frac{1,000}{(1 + r)^{24}}$

3. Solve for $r$ (semiannual yield): This is typically done using trial and error or a financial calculator. However, to simplify the process, I will provide a direct solution:

Using a financial calculator or an iterative approach (or a solver), you would find the semiannual yield ($r$) to be approximately 5.57%.

4. Convert to annual yield to maturity (YTM): Since the yield is semiannual, we multiply by 2 to get the annual YTM:

$YTM = 5.57\% \times 2 = 11.14\%$

Conclusion:

The Yield to Maturity (YTM) of the bond is approximately 11.14% annually.

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Would you like further details on how to calculate this using financial calculators, or have other questions?

Here are some related questions for deeper understanding:

1. How do callable bonds affect the yield to maturity calculation?
2. What is the difference between Yield to Maturity (YTM) and Yield to Call (YTC)?
3. How would the YTM change if the bond price were lower than $1,096?
4. How is the bond price related to interest rates in the context of YTM?
5. How do you calculate Yield to Call (YTC) for callable bonds?

Tip: Financial calculators and spreadsheet functions (like Excel's YIELD function) are very useful for quickly calculating YTM, especially when dealing with more complex bond structures.