You find a zero coupon bond with a par value of $10,000 and 20 years to maturity. The yield to
maturity on this bond is 4.2 percent. Assume semiannual compounding periods. What is the price of
the bond?

To calculate the price of a zero-coupon bond, we use the formula:

\[
P = \frac{F}{(1 + \frac{r}{n})^{n \cdot t}}
\]

Where:
- $ P $ = Price of the bond
- $ F $ = Face (par) value of the bond = $10,000
- $ r $ = Annual yield to maturity = 4.2% or 0.042
- $ n $ = Number of compounding periods per year (semiannual, so $ n = 2 $)
- $ t $ = Time to maturity in years = 20 years

Now, let's plug in the values and compute the price:

\[
P = \frac{10,000}{(1 + \frac{0.042}{2})^{2 \cdot 20}}
\]

Let's calculate this step-by-step.The price of the zero-coupon bond is approximately **$4,354.82**.

Would you like further clarification or details on this calculation? Here are some related questions:

1. How does the yield to maturity affect bond prices?
2. What happens to the bond price if the compounding period changes?
3. How would the bond price change if the yield to maturity increases to 5%?
4. What is the relationship between time to maturity and bond price?
5. How is a zero-coupon bond different from a regular coupon bond?

**Tip:** Zero-coupon bonds are typically sold at a discount to face value, and the difference between the purchase price and par value represents the interest earned.

You find a zero coupon bond with a par value of $10,000 and 20 years to maturity. The yield to maturity on this bond is 4.2 percent. Assume semiannual compounding periods. What is the price of the bond?

Learn how to calculate the price of a zero-coupon bond with a $10,000 face value, 20 years to maturity, and a 4.2% yield to maturity using semiannual compounding. This detailed step-by-step solution covers key financial concepts such as bond pricing and compound interest.

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