If a bond's yield to maturity does not change, the return on the bond each year will be equal to the yield to maturity. Confirm this for both a premium and a discount bond using a 4-year 3.2 percent coupon bond with annual coupon payments and a face value of $1,000.

 

a. Assume the yield to maturity is 2.2 percent.

 

What is the current value of the bond?

To confirm that the return on the bond each year will be equal to the yield to maturity (YTM), we can first calculate the bond's current value using the given information:

- **Face value (F)** = $1,000
- **Coupon rate** = 3.2%
- **Annual coupon payment (C)** = 3.2% of $1,000 = $32
- **Time to maturity (N)** = 4 years
- **Yield to maturity (YTM)** = 2.2%

The current value of the bond can be calculated using the present value formula for bonds:

\[
P = \sum_{t=1}^{N} \frac{C}{(1 + \text{YTM})^t} + \frac{F}{(1 + \text{YTM})^N}
\]

Where:
- $ P $ is the current price of the bond
- $ C $ is the annual coupon payment
- $ F $ is the face value
- $ \text{YTM} $ is the yield to maturity
- $ N $ is the number of years to maturity

Let’s break this down:

1. The present value of the coupon payments is:

\[
\text{PV of coupons} = \sum_{t=1}^{4} \frac{32}{(1 + 0.022)^t}
\]

2. The present value of the face value is:

\[
\text{PV of face value} = \frac{1,000}{(1 + 0.022)^4}
\]

Now, let’s calculate:

\[
P =  \frac{32}{(1.022)^1} + \frac{32}{(1.022)^2} + \frac{32}{(1.022)^3} + \frac{32}{(1.022)^4} + \frac{1,000}{(1.022)^4}
\]

I'll compute the bond price now.The current value of the bond is approximately **$1,037.89**.

Since this value is higher than the bond's face value of $1,000, the bond is trading at a **premium**. 

Would you like a more detailed breakdown of the calculations? Let me know if you have any other questions.

Here are 5 related questions:
1. How does the price of a bond change when the yield to maturity increases?
2. What happens to a bond's price as it approaches its maturity date?
3. How does a bond's duration relate to its price sensitivity to interest rate changes?
4. Can a bond with a lower coupon rate than the YTM trade at a premium?
5. How does reinvestment risk affect bond returns?

**Tip:** The bond's price and its yield to maturity are inversely related — when one goes up, the other goes down.

If a bond's yield to maturity does not change, the return on the bond each year will be equal to the yield to maturity. Confirm this for both a premium and a discount bond using a 4-year 3.2 percent coupon bond with annual coupon payments and a face value of $1,000. Assume the yield to maturity is 2.2 percent. What is the current value of the bond?

Explore how to calculate the current value of a 4-year, 3.2% coupon bond with a face value of $1,000 and a yield to maturity of 2.2%. Includes detailed steps on bond pricing, present value of coupon payments, and face value discounting. Learn key finance concepts like Yield to Maturity and Present Value.

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