.   Assuming semiannual compounding, a 12-year zero coupon bond with a par value of $1,000 and an annual required return of 9% would be priced around $______. (Hint: You should convert the annual required rate of return into a semiannual rate before discounting the zero’s par value.)

To calculate the price of a zero-coupon bond with semiannual compounding, we can use the following formula:

\[
P = \dfrac{F}{(1 + r/n)^{nt}}
\]

Where:
- $P$ = Price of the bond (what we're solving for)
- $F$ = Par value of the bond = \$1,000
- $r$ = Annual required return = 9% or 0.09
- $n$ = Number of compounding periods per year = 2 (since it's semiannual compounding)
- $t$ = Number of years to maturity = 12

### Step 1: Convert the annual required return to a semiannual rate.
Since interest is compounded semiannually, we divide the annual return by 2:

\[
\text{Semiannual rate} = \dfrac{0.09}{2} = 0.045
\]

### Step 2: Calculate the total number of semiannual periods.
There are 12 years to maturity, and with semiannual compounding, there are 2 periods per year. So:

\[
\text{Total periods} = 12 \times 2 = 24
\]

### Step 3: Apply the formula.
Now substitute the values into the formula:

\[
P = \dfrac{1,000}{(1 + 0.045)^{24}}
\]

I'll calculate the bond price next.The price of the 12-year zero-coupon bond with semiannual compounding and an annual required return of 9% would be approximately **$347.70**.

Would you like more details or have any further questions? Here are five related questions that could help deepen understanding:

1. How would the price change if the required return were higher or lower?
2. What is the relationship between bond price and time to maturity in a zero-coupon bond?
3. How would the price differ if compounding were annual instead of semiannual?
4. What is the significance of a zero-coupon bond compared to a coupon-bearing bond?
5. How would inflation impact the real return on this bond?

**Tip:** The longer the time to maturity, the more sensitive a bond's price becomes to changes in interest rates.

Assuming semiannual compounding, a 12-year zero coupon bond with a par value of $1,000 and an annual required return of 9% would be priced around $______. (Hint: You should convert the annual required rate of return into a semiannual rate before discounting the zero’s par value.)

Learn how to calculate the price of a zero-coupon bond with a par value of $1,000, 12 years to maturity, and an annual required return of 9%. This solution breaks down the calculation using the compound interest formula, considering semiannual compounding. Suitable for finance and business 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