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 dollar price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
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 dollar price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Problem 7-9 Zero Coupon Bonds [LO2]**
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 dollar price of the bond? *(Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)*
[Bond price]
---
**Explanation:**
To find the price of a zero coupon bond, you need to calculate its present value (PV) using the formula for present value of a single sum:
\[ PV = \frac{FV}{(1 + r/n)^{nt}} \]
Where:
- \( FV \) is the future value or par value of the bond ($10,000).
- \( r \) is the annual yield to maturity (4.2% or 0.042).
- \( n \) is the number of compounding periods per year (2 for semiannual).
- \( t \) is the number of years to maturity (20).
Plug in the values to find the bond price, ensuring you do not round intermediate calculations and round the final answer to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2e6bca0-5751-4e3b-9150-515606817feb%2Ffff7e5d7-4a40-4b27-b1d5-2ea950cc4f73%2F7v1j9gl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 7-9 Zero Coupon Bonds [LO2]**
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 dollar price of the bond? *(Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)*
[Bond price]
---
**Explanation:**
To find the price of a zero coupon bond, you need to calculate its present value (PV) using the formula for present value of a single sum:
\[ PV = \frac{FV}{(1 + r/n)^{nt}} \]
Where:
- \( FV \) is the future value or par value of the bond ($10,000).
- \( r \) is the annual yield to maturity (4.2% or 0.042).
- \( n \) is the number of compounding periods per year (2 for semiannual).
- \( t \) is the number of years to maturity (20).
Plug in the values to find the bond price, ensuring you do not round intermediate calculations and round the final answer to two decimal places.
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