Broke Benjamin Company has a bond outstanding that makes semiannual payments with a coupon rate of 6.4 percent. The bond sells for $1,043.47 and matures in 20 years. The par value is $1,000. What is the YTM of the bond?

To calculate the Yield to Maturity (YTM) of a bond, we use the following general approach:

\[
YTM = \text{the rate that equates the present value of the bond's cash flows to its price}.
\]

In this case:
- **Coupon rate (annual)** = 6.4% → semiannual coupon = $ \frac{6.4\%}{2} = 3.2\% $ of the face value per period.
- **Par value (Face value)** = $1,000.
- **Bond price (current price)** = $1,043.47.
- **Maturity** = 20 years → semiannual periods = $ 20 \times 2 = 40 $ periods.
- **Coupon payment per period** = $ 1,000 \times \frac{6.4\%}{2} = 32 $ dollars.

We need to find the semiannual YTM and then convert it to an annual rate.

### Bond pricing equation:
The bond price can be represented as the sum of the present value of the coupon payments and the present value of the face value (par) at maturity:

\[
\text{Bond Price} = \sum_{t=1}^{40} \frac{C}{(1+r)^t} + \frac{F}{(1+r)^{40}}
\]
Where:
- $ C = 32 $ (semiannual coupon payment),
- $ F = 1,000 $ (face value),
- $ r $ = semiannual YTM (what we need to solve),
- $ t $ = 40 periods.

Now, we'll solve this iteratively (or using a financial calculator). For now, I’ll use an iterative approach:

Using a trial-and-error method or a calculator, we get the YTM:

\[
\text{YTM (semiannual)} \approx 3.0\% \text{ per half-year}.
\]

Thus, the **annual YTM** is:

\[
YTM = 3.0\% \times 2 = 6.0\% \text{ annually}.
\]

### Conclusion:
The YTM of the bond is approximately **6.0% per year**.

Would you like further details or clarifications?

Here are 5 related questions to expand your understanding:
1. How does the price of a bond change when the YTM increases?
2. What is the relationship between a bond's coupon rate and its YTM when the bond sells at a premium?
3. How can YTM be interpreted for zero-coupon bonds?
4. What is the difference between current yield and YTM?
5. How does the frequency of coupon payments affect the calculation of YTM?

**Tip**: When bond prices are above face value (premium), the YTM will generally be lower than the coupon rate.

Determine the Yield to Maturity (YTM) for a Broke Benjamin Company bond that makes semiannual payments with a 6.4% coupon rate. The bond is priced at $1,043.47, matures in 20 years, and has a par value of $1,000. Understand key financial concepts like bond valuation and the time value of money, suitable for finance students.

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