A bond is issued with a coupon of 4% paid annually, a maturity of 30 years, and a yield to maturity of 7%. What rate of return will be earned by an investor who purchases the bond for $627.73 and holds it for 1 year if the bond's yield to maturity at the end of the year is 8%.
Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.

To determine the rate of return earned by an investor who purchases the bond and holds it for 1 year, we need to account for both the coupon payment and the change in the bond's price over the year. Here's a step-by-step breakdown of the calculation:

### Step 1: Identify the relevant information
- **Coupon Rate (C):** 4% of face value (assume the bond has a face value of $1000)
- **Annual Coupon Payment (P):** $ 4\% \times 1000 = 40 $
- **Initial Bond Price (P_0):** $627.73
- **Yield to Maturity (YTM) at purchase:** 7%
- **Yield to Maturity (YTM) at the end of 1 year:** 8%
- **Maturity:** 30 years

### Step 2: Find the bond price after 1 year
The bond price at the end of the year can be calculated using the yield to maturity (YTM) at that time (8%) and the remaining time to maturity (29 years, since 1 year has passed). The price of a bond is the present value of its future coupon payments and face value discounted at the YTM.

The formula for bond price is:

\[
P = C \times \left(1 - \frac{1}{(1 + YTM)^n}\right) + \frac{F}{(1 + YTM)^n}
\]

Where:
- $ P $ = bond price
- $ C $ = annual coupon payment ($40)
- $ F $ = face value ($1000)
- $ n $ = number of years to maturity (29)
- $ YTM $ = new yield to maturity (8% or 0.08)

Let's calculate this bond price.The bond price at the end of the year, after 1 year of holding and with a yield to maturity of 8%, is approximately **$553.66**.

### Step 3: Calculate the rate of return
The rate of return (RoR) is calculated by considering the coupon payment and the capital gain or loss from holding the bond for one year. The formula for rate of return is:

\[
RoR = \frac{{\text{{Coupon Payment}} + (\text{{Price at End of Year}} - \text{{Initial Price}})}}{{\text{{Initial Price}}}} \times 100
\]

Substituting the known values:

- Coupon Payment = $40
- Price at End of Year = $553.66
- Initial Price = $627.73

Let's compute the rate of return.The rate of return earned by the investor after holding the bond for 1 year is approximately **-5.43%**. This negative return reflects both the coupon payment and the capital loss due to the bond price decreasing as the yield to maturity increased from 7% to 8%.

Do you want any additional details or have questions about this result?

Here are 5 related questions to deepen your understanding:
1. How does the yield to maturity affect bond prices over time?
2. What is the relationship between coupon rates and bond prices?
3. How would the rate of return change if the yield to maturity had decreased instead?
4. How does holding a bond to maturity differ from selling it early in terms of returns?
5. What are the risks associated with investing in long-term bonds?

**Tip:** When yields rise, bond prices fall. This inverse relationship is crucial when considering short-term investments in bonds.

A bond is issued with a coupon of 4% paid annually, a maturity of 30 years, and a yield to maturity of 7%. What rate of return will be earned by an investor who purchases the bond for $627.73 and holds it for 1 year if the bond's yield to maturity at the end of the year is 8%?

Learn how to calculate the rate of return on a bond with a 4% coupon, a 30-year maturity, and changing yields. This example shows the impact of yield to maturity on bond pricing, with detailed formulas and a final rate of return of -5.43%. Suitable for finance students.

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