Suppose a bond with a par value of $1,000 has coupon of 3.85%. What is the nominal value (in dollars) of the bond if the current interest rate is 5.35%? Round to the nearest dollar. (See Example 5 in this section.)


To determine the nominal value of the bond given that its coupon rate is 3.85% and the current interest rate is 5.35%, we can apply the bond pricing formula, which is based on the present value of its future cash flows (coupons) and its face value at maturity.

The formula for the price of a bond is:

\[
\text{Price of bond} = \left( \frac{C}{r} \right) \times \left( 1 - \frac{1}{(1 + r)^t} \right) + \frac{F}{(1 + r)^t}
\]

Where:
- $ C $ is the annual coupon payment
- $ r $ is the current interest rate (as a decimal)
- $ t $ is the number of years to maturity
- $ F $ is the face value (par value) of the bond

However, since no maturity period is specified in the problem, we'll use a simpler approach called the **current yield** method, assuming the bond is a perpetuity (no maturity).

**Step 1: Calculate the annual coupon payment:**

\[
C = \text{Coupon rate} \times \text{Face value} = 3.85\% \times 1,000 = 0.0385 \times 1,000 = 38.50
\]

**Step 2: Use the current yield formula to find the bond's price:**

The bond's price can be approximated by:

\[
\text{Price of bond} = \frac{\text{Annual coupon payment}}{\text{Current interest rate}}
\]

Substitute the values:

\[
\text{Price of bond} = \frac{38.50}{0.0535} = 719.63
\]

Rounding to the nearest dollar:

\[
\text{Price of bond} \approx 720
\]

Thus, the nominal value of the bond is **$720**.

---

Would you like more details or have any questions about this calculation?  
Here are some related questions for deeper exploration:

1. How does the bond's price change if the current interest rate decreases to 4%?
2. What would be the nominal value of the bond if its coupon rate were 6% instead?
3. How is the duration of a bond related to its sensitivity to interest rate changes?
4. Can you explain the difference between the bond's nominal yield and its current yield?
5. What factors influence the market price of a bond apart from interest rates?

**Tip:** The price of a bond moves inversely to interest rates—when rates rise, bond prices fall, and when rates fall, bond prices increase.

Suppose a bond with a par value of $1,000 has coupon of 3.85%. What is the nominal value (in dollars) of the bond if the current interest rate is 5.35%? Round to the nearest dollar.

Learn how to calculate the nominal value of a bond with a par value of $1,000, a coupon rate of 3.85%, and a current interest rate of 5.35%. This problem covers bond pricing concepts, including the current yield method, and is ideal for 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