What would you pay for a bond that pays an annual coupon of $45, has a face value of $1,000, matures in 11 years, and has a yield to maturity of 10%?

To find the price of the bond, we can use the **present value formula** for bonds, which involves calculating the present value of the coupon payments and the present value of the face value (par value) at maturity.

The formula for the price of the bond is:

\[
P = C \times \left(1 - \frac{1}{(1 + r)^t}\right) \div r + \frac{F}{(1 + r)^t}
\]

Where:
- $ P $ = price of the bond
- $ C $ = annual coupon payment
- $ F $ = face value (or par value)
- $ r $ = yield to maturity (as a decimal)
- $ t $ = number of years until maturity

**Given:**
- Annual coupon payment $ C = 45 $ dollars
- Face value $ F = 1,000 $ dollars
- Yield to maturity $ r = 10\% = 0.10 $
- Number of years $ t = 11 $

Let’s calculate the price of the bond using this formula.

First, we will compute the present value of the coupon payments, then the present value of the face value, and sum them together.The price you would pay for the bond is approximately **$642.77**.

Would you like further details or have any questions? 

Here are 5 related questions you might find useful:
1. How does a change in yield to maturity affect the price of a bond?
2. What is the difference between coupon rate and yield to maturity?
3. How do you calculate the current yield of a bond?
4. What are zero-coupon bonds, and how are they priced?
5. What happens to bond prices when interest rates rise?

**Tip**: The price of a bond moves inversely to the yield to maturity. If the yield increases, the bond price decreases, and vice versa.

Learn how to calculate the price of a bond with an annual coupon of $45, a face value of $1,000, and a maturity of 11 years, given a yield to maturity of 10%. This solution covers key concepts in bond valuation, including the present value of coupon payments and face value. Suitable for undergraduate finance or economics students.

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