 The market price is ​$1 comma 075 for a 19​-year bond ​($1 comma 000 par​ value) that pays 11 percent annual​ interest, but makes interest payments on a semiannual basis ​(5.5 percent​ semiannually).  What is the​ bond's yield to​ maturity?

To calculate the bond's yield to maturity (YTM), we need to solve the following equation, which equates the bond's current price to the present value of its future cash flows. The cash flows include the semiannual interest payments and the face value (par value) at maturity.

Given:
- Bond price ($P$) = $1,075
- Face value ($F$) = $1,000
- Annual coupon rate = 11% (which means the semiannual coupon rate is 5.5%)
- Number of years to maturity ($n$) = 19 years (which means 38 semiannual periods)

The semiannual coupon payment ($C$) is:
\[
C = \frac{11\% \times 1000}{2} = 55 \text{ dollars}
\]

The bond price equation is:

\[
P = \sum_{t=1}^{38} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^{38}}
\]

Where:
- $P$ is the bond's price ($1,075)
- $C$ is the semiannual coupon payment ($55)
- $F$ is the face value ($1,000)
- $r$ is the semiannual yield to maturity
- $t$ is the number of semiannual periods

This is a complex equation to solve directly by hand, so we'll typically use a financial calculator or numerical methods (such as Excel's RATE function or iterative solving) to find $r$, which can then be annualized to find the YTM.

Let's solve for the semiannual yield to maturity using numerical methods and then annualize it to get the YTM.

Calculating...The bond's yield to maturity (YTM) is approximately **10.10%** per year.

Would you like more details on how this was calculated, or do you have any further questions?

Here are some related questions that might interest you:

1. How does the yield to maturity compare to the current yield of a bond?
2. What factors can cause a bond's yield to maturity to change over time?
3. How does the yield to maturity differ for bonds with different maturities?
4. What are the risks associated with investing in bonds with a high YTM?
5. How do changes in interest rates affect the YTM of a bond?

**Tip:** The yield to maturity assumes that all coupon payments are reinvested at the same rate as the bond's current yield. This might not always be possible, depending on market conditions.

Learn how to calculate the yield to maturity (YTM) of a bond priced at $1,075 with a $1,000 par value and an annual coupon rate of 11% (5.5% semiannually). Understand the formula used for bond valuation and the steps involved in determining YTM. Suitable for undergraduate students and finance professionals.

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