To calculate the one-year return on a bond, we need to combine the bond's coupon payment and the capital gain or loss from holding the bond for a year. Here's how we can break it down:

Step 1: Calculate the Annual Coupon Payment

The bond's coupon payment is based on the coupon rate applied to the face value:

$\text{Coupon Payment} = \text{Face Value} \times \text{Coupon Rate} = 7000 \times 0.10 = 700$

Step 2: Calculate the Price of the Bond (Present Value) Using the Market Rate

We need to find the present value (price) of the bond when the market rate is 8%. The bond has 5 years left to maturity, so we discount the coupon payments and the face value over 5 years at the market rate.

The bond price $P$ is the sum of:

• The present value of the coupon payments, and
• The present value of the face value at maturity.

$P = \left( \sum_{t=1}^{5} \frac{\text{Coupon Payment}}{(1+\text{Market Rate})^t} \right) + \frac{\text{Face Value}}{(1+\text{Market Rate})^5}$

Using this formula, let's calculate the bond price:

$P = \left( \sum_{t=1}^{5} \frac{700}{(1+0.08)^t} \right) + \frac{7000}{(1+0.08)^5}$

Let's calculate that now.The current price of the bond, given the market rate of 8%, is approximately $7558.98.

Step 3: Calculate the Bond Price After One Year

After one year, the bond will have 4 years left to maturity. We will now calculate the bond price after 1 year, using the same approach but with 4 years instead of 5.

$P_{\text{after 1 year}} = \left( \sum_{t=1}^{4} \frac{700}{(1+0.08)^t} \right) + \frac{7000}{(1+0.08)^4}$

Let's calculate this now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through the remaining steps to calculate the one-year return manually if you'd like to follow along:

1. Calculate the bond price after one year as explained previously.
2. Calculate the one-year capital gain by finding the difference between the bond's price after one year and its current price.
3. Add the coupon payment to the capital gain to get the total one-year return.
4. Divide this total return by the bond price at the beginning of the year to get the rate of return.

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