Leonard Cooper is looking to invest in a two-year bond from Big Bang Productions Corporation. The company makes semi-annual coupon payments of $67.00 (every 6 months) with a face value of $1,000. If the market price of the bonds is $1,072.00, what yield to maturity will Leonard earn (express as an EAR)?

To calculate the **Yield to Maturity (YTM)** of a bond and express it as an **Effective Annual Rate (EAR)**, we need to follow several steps. The bond's characteristics are as follows:

- **Coupon payments (semi-annual):** \$67.00
- **Face value:** \$1,000
- **Current market price:** \$1,072.00
- **Term:** 2 years (4 semi-annual periods)

### Step 1: Calculate Semi-Annual Yield to Maturity (YTM)

The YTM can be found using the following formula for bond pricing:

\[
P = \frac{C}{(1 + r)^1} + \frac{C}{(1 + r)^2} + \cdots + \frac{C}{(1 + r)^n} + \frac{F}{(1 + r)^n}
\]

Where:
- $ P $ = Current price of the bond = \$1,072.00
- $ C $ = Semi-annual coupon payment = \$67.00
- $ F $ = Face value = \$1,000
- $ r $ = Semi-annual YTM (to be determined)
- $ n $ = Total number of periods = 4 (2 years × 2 periods per year)

We will solve for $ r $ (the semi-annual YTM) using this formula.

### Step 2: Convert Semi-Annual YTM to Effective Annual Rate (EAR)

Once we have the semi-annual YTM, we convert it to an EAR using the following formula:

\[
EAR = (1 + r_{semi})^2 - 1
\]

Where:
- $ r_{semi} $ is the semi-annual YTM.

Now, let's solve this numerically.The **Effective Annual Rate (EAR)** that Leonard Cooper will earn on the bond is approximately **9.59%**.

Do you have any questions, or would you like more details on this calculation?

Here are 5 related questions you might find useful:
1. How does the bond's price affect its yield to maturity (YTM)?
2. What is the difference between nominal yield and yield to maturity?
3. How does compounding frequency impact the effective annual rate (EAR)?
4. Can YTM change if market interest rates fluctuate?
5. What factors can cause the market price of a bond to differ from its face value?

**Tip:** Remember that the bond's YTM assumes that all coupon payments are reinvested at the same yield, which may not always happen in practice.

Learn how to calculate the Yield to Maturity (YTM) and Effective Annual Rate (EAR) for a two-year bond from Big Bang Productions Corporation with semi-annual coupon payments. Understand key finance concepts and formulas involved in bond pricing and investment analysis.

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