Nikita Enterprises has bonds on the market making annual payments, with 17 years to maturity, a par value of $1,000, and selling for $969. At this price, the bonds yield 8.1 percent. What must the coupon rate be on the bonds?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.



To find the coupon rate on the bonds, we can use the following bond pricing formula:

\[
P = \frac{C \times (1 - (1 + r)^{-t})}{r} + \frac{F}{(1 + r)^t}
\]

Where:
- $ P $ = price of the bond ($969)
- $ C $ = annual coupon payment (what we're solving for)
- $ r $ = yield to maturity (8.1% or 0.081)
- $ t $ = time to maturity (17 years)
- $ F $ = par value of the bond ($1,000)

We know the price $ P $, the yield to maturity $ r $, the time $ t $, and the face value $ F $. The goal is to solve for $ C $, the annual coupon payment, and then use it to find the coupon rate.

### Step 1: Rearrange the formula to isolate $ C $.

The formula can be separated into two parts: the present value of the coupon payments and the present value of the par value:

\[
969 = \frac{C \times (1 - (1 + 0.081)^{-17})}{0.081} + \frac{1000}{(1 + 0.081)^{17}}
\]

### Step 2: Solve for $ C $, the annual coupon payment. 

I'll calculate this now.The annual coupon payment $ C $ is approximately $77.58.

### Step 3: Calculate the coupon rate.
The coupon rate is calculated as:

\[
\text{Coupon Rate} = \frac{C}{F} \times 100
\]

Let me calculate the coupon rate.The coupon rate on the bonds is approximately **7.76%**.

Would you like further details or explanations on this? Here are some related questions you might find useful:

1. How does the yield to maturity affect bond pricing?
2. What happens to the bond price if the coupon rate exceeds the yield to maturity?
3. How can you calculate the price of a bond with semi-annual coupon payments?
4. How does the time to maturity influence a bond’s price and yield?
5. What is the relationship between interest rates and bond prices?

**Tip:** The bond price will decrease as the yield to maturity increases, and vice versa, due to the inverse relationship between bond prices and interest rates.

Nikita Enterprises has bonds on the market making annual payments, with 17 years to maturity, a par value of $1,000, and selling for $969. At this price, the bonds yield 8.1 percent. What must the coupon rate be on the bonds?

Learn how to calculate the coupon rate for Nikita Enterprises bonds, which have 17 years to maturity, a par value of $1,000, and sell for $969. This problem covers bond pricing formulas and the concept of yield to maturity, suitable for advanced high school or college students.

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