Consider a bond with semi-annual coupon rate (cr) of 9 percent. The par value is $1,000, and the bond has 6 years to maturity. If current market price is $900, what is yield to maturity (YTM)?

To calculate the yield to maturity (YTM) of a bond, we use the following variables:

- $ C $: Semi-annual coupon payment
- $ F $: Face value (or par value) of the bond
- $ P $: Current market price of the bond
- $ n $: Number of periods until maturity
- $ YTM $: The yield to maturity, which we need to solve for

### Step 1: Gather the known values
- Coupon rate $ cr = 9\% $ (annual coupon rate)
- Face value $ F = 1,000 $
- Market price $ P = 900 $
- Time to maturity $ = 6 $ years
- Since the bond pays semi-annual coupons, $ n = 6 \times 2 = 12 $ periods
- The coupon payment per period is:
  \[
  C = \frac{cr \times F}{2} = \frac{9\% \times 1,000}{2} = \frac{90}{2} = 45
  \]

### Step 2: The bond pricing formula
The bond price is the present value of its future coupon payments and the present value of the par value at maturity. The formula is:

\[
P = \sum_{t=1}^{n} \frac{C}{(1 + \frac{YTM}{2})^t} + \frac{F}{(1 + \frac{YTM}{2})^n}
\]

Where:
- $ P $: Current bond price
- $ C $: Coupon payment per period
- $ F $: Face value of the bond
- $ YTM $: Yield to maturity per period
- $ n $: Number of periods

### Step 3: Solving for YTM
This equation is non-linear and cannot be solved algebraically, so we must either use a financial calculator or iterative methods like trial and error, Newton's method, or numerical techniques to find $ YTM $.

Let me calculate this numerically for you.The yield to maturity (YTM) for the bond is approximately **11.34%** (annualized).

Would you like more details on this process or clarification on any specific step?

Here are five related questions you might consider:
1. How would the YTM change if the bond price increased to $950?
2. How does the coupon frequency affect the yield to maturity?
3. What is the relationship between YTM and bond prices?
4. How would the bond's YTM compare to the coupon rate in case of premium pricing?
5. What is the difference between current yield and yield to maturity?

**Tip**: A bond's price and its YTM are inversely related — as the bond price decreases, the YTM increases, and vice versa.

This guide explains how to calculate the yield to maturity (YTM) for a bond with a semi-annual coupon rate of 9%. The bond has a face value of $1,000, 6 years to maturity, and is currently priced at $900. Learn key concepts like bond valuation, time value of money, and the inverse relationship between bond prices and yields. Suitable for finance and business students.

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