Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 9 percent, has a YTM of 7 percent, and has 15 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 7 percent, has a YTM of 9 percent, and also has 15 years to maturity. The bonds have a $1,000 par value.
 
What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In six years? In 11 years? In 13 years? In 15 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

To calculate the price of the bonds, we will use the **present value of future cash flows formula**. This formula takes into account the periodic coupon payments and the principal repayment at maturity, discounted by the yield to maturity (YTM).

The price of a bond is given by the formula:

\[
\text{Bond Price} = C \times \left( 1 - \frac{1}{(1 + r)^n} \right) \div r + \frac{F}{(1 + r)^n}
\]

Where:
- $ C $ = Semiannual coupon payment = $ \frac{\text{Coupon Rate} \times \text{Face Value}}{2} $
- $ F $ = Face value of the bond (par value, typically $1,000)
- $ r $ = Semiannual yield to maturity (YTM/2)
- $ n $ = Total number of semiannual periods to maturity (years to maturity × 2)

We will calculate for Bond X and Bond Y.

### For Bond X (Premium Bond):
- **Coupon rate**: 9% annually, so semiannual coupon = 9%/2 × 1000 = $45
- **YTM**: 7% annually, so semiannual YTM = 7%/2 = 0.035
- **Years to maturity**: 15 years, so $ n = 15 \times 2 = 30 $

### For Bond Y (Discount Bond):
- **Coupon rate**: 7% annually, so semiannual coupon = 7%/2 × 1000 = $35
- **YTM**: 9% annually, so semiannual YTM = 9%/2 = 0.045
- **Years to maturity**: 15 years, so $ n = 15 \times 2 = 30 $

Next, I will calculate the price of each bond today and at different times in the future.Here are the prices for Bond X (premium bond) and Bond Y (discount bond) today and at different future points in time:

### Bond X (Premium Bond):
- **Price today**: \$1,183.92
- **Price in 1 year**: \$1,176.67
- **Price in 6 years**: \$1,131.90
- **Price in 11 years**: \$1,068.74
- **Price in 13 years**: \$1,036.73
- **Price in 15 years (at maturity)**: \$1,000.00

### Bond Y (Discount Bond):
- **Price today**: \$837.11
- **Price in 1 year**: \$842.57
- **Price in 6 years**: \$878.40
- **Price in 11 years**: \$934.04
- **Price in 13 years**: \$964.12
- **Price in 15 years (at maturity)**: \$1,000.00

As we see, Bond X (a premium bond) gradually decreases in price as it approaches maturity, converging to its par value of \$1,000. Bond Y (a discount bond) increases in price over time as it approaches par value.

Would you like to explore more details or clarify any steps?

Here are 5 related questions to expand your understanding:
1. How does the relationship between coupon rate and YTM affect bond prices?
2. Why do premium bonds decrease in price while discount bonds increase over time?
3. How would changes in interest rates affect the bond prices?
4. What role does the time to maturity play in determining a bond's price sensitivity?
5. How can duration and convexity provide further insights into bond price movements?

**Tip:** Bonds with longer maturities are more sensitive to changes in interest rates. This is known as interest rate risk.

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 9 percent, has a YTM of 7 percent, and has 15 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 7 percent, has a YTM of 9 percent, and also has 15 years to maturity. The bonds have a $1,000 par value.

What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In six years? In 11 years? In 13 years? In 15 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Calculate the prices of premium Bond X and discount Bond Y today and at future points in time, given their coupon rates, YTM, and 15-year maturity. Learn the detailed step-by-step bond pricing method using present value formulas. Suitable for finance students at the undergraduate level.

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