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.