To determine the price of the bond, we use the bond pricing formula, which discounts all future cash flows (coupons and par value) back to the present at the bond's yield to maturity (YTM). Here are the details of the bond:

• Par value (Face value): $1,000
• Coupon rate: 8.16% (paid semi-annually, so divide by 2 for each payment)
• Yield to maturity (YTM): 7.65% (also semi-annual, so divide by 2)
• Time to maturity: 17 years (34 semi-annual periods)

Step 1: Determine Semi-Annual Coupon Payment and YTM

1. Semi-annual coupon rate = $\frac{8.16\%}{2} = 4.08\%$
2. Coupon payment = $4.08\% \times 1,000 = 40.80$
3. Semi-annual YTM = $\frac{7.65\%}{2} = 3.825\%$ or 0.03825 in decimal form

Step 2: Determine the Number of Periods

• Since it's a 17-year bond with semi-annual payments, there are $17 \times 2 = 34$ periods.

Step 3: Bond Pricing Formula

The price of a bond (PV) is given by:

$PV = \sum_{t=1}^{34} \frac{C}{(1 + y)^t} + \frac{F}{(1 + y)^{34}}$

where:

• $C$ is the semi-annual coupon payment ($40.80),
• $y$ is the semi-annual YTM (0.03825),
• $F$ is the face value ($1,000),
• $t$ is the total number of periods (34).

The formula can be simplified to:

$PV = \frac{C \times (1 - (1 + y)^{-n})}{y} + \frac{F}{(1 + y)^n}$

Plugging in the values:

$PV = \frac{40.80 \times (1 - (1 + 0.03825)^{-34})}{0.03825} + \frac{1,000}{(1 + 0.03825)^{34}}$

Let me calculate this for the exact bond price.The price of the bond is approximately $1,048.06.

Would you like further details on the calculation steps or explanations? Here are some related questions that might interest you:

1. How would the bond price change if the coupon rate were higher?
2. What happens to bond prices when the yield to maturity increases?
3. How would this bond's price differ if it paid interest annually instead of semi-annually?
4. What is the relationship between bond price and time to maturity?
5. How would a change in market interest rates affect the bond's price?

Tip: Remember that when the yield to maturity is less than the coupon rate, the bond price is above its par value (a premium bond).