Calculate one year returns on a bond that has a term of 5 years, a face value of $7000, offers a coupon rate of 10% and the market rate is 8%. The rate of return is:
		18.92%
		16.62%
		15.15%
		12.45%


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.

Would you like further assistance on this?

Calculate one year returns on a bond that has a term of 5 years, a face value of $7000, offers a coupon rate of 10% and the market rate is 8%. The rate of return is: 18.92%, 16.62%, 15.15%, 12.45%

Learn how to calculate the one-year return on a bond with a 5-year term, face value of $7000, a coupon rate of 10%, and a market rate of 8%. This problem covers concepts such as bond valuation, coupon payments, capital gains, and discounting cash flows. Suitable for Grades 11-12 and college-level finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation