5 year semiannual coupon bond with a face value of $1,000 trades at $912. The market determined discount rate is 8%. What is the coupon rate? Answer in percent and round to two decimal places

To find the coupon rate of the bond, we use the present value formula for a semiannual coupon bond. The formula for the price of a bond is:

\[
P = \frac{C}{1 + r} + \frac{C}{(1 + r)^2} + \cdots + \frac{C + F}{(1 + r)^n}
\]

Where:
- $P$ is the price of the bond ($912),
- $C$ is the semiannual coupon payment,
- $r$ is the semiannual discount rate (8% annually means 4% semiannually, or 0.04),
- $F$ is the face value ($1,000),
- $n$ is the total number of periods (5 years × 2 = 10 periods).

Given this, we will rearrange the formula to solve for the coupon payment $C$, then use $C$ to find the coupon rate.

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Here are some related questions you may also find helpful:

1. How do bond prices react to changes in interest rates?
2. What is the difference between coupon rate and yield to maturity?
3. How does a bond's time to maturity affect its price sensitivity to interest rates?
4. What are zero-coupon bonds, and how do they differ from regular coupon bonds?
5. How is the present value of bond cash flows calculated?

**Tip:** Always ensure to distinguish between the annual and semiannual rates when working with bonds that make semiannual payments.

5 year semiannual coupon bond with a face value of $1,000 trades at $912. The market determined discount rate is 8%. What is the coupon rate? Answer in percent and round to two decimal places.

Learn how to calculate the coupon rate for a 5-year semiannual coupon bond with a face value of $1,000, trading at $912, with an 8% annual discount rate. This tutorial covers bond valuation, present value of cash flows, and discount rate calculations. Suitable for finance students at the college level.

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