Asked by Marlee Joudrey on Jul 06, 2024
Verified
Suppose you purchase a zero-coupon bond with face value $1,000, maturing in 20 years, for $214.51. If the yield to maturity on the bond remains unchanged, what will the price of the bond be five years from now?
A) $315.20
B) $387.52
C) $410.91
D) $680.58
E) $1,000.00
Zero-Coupon Bond
A Zero-Coupon Bond is a debt security that doesn't pay interest (a coupon) but is traded at a deep discount, rendering profit at maturity when the bond is redeemed for its full face value.
Yield To Maturity
The total return anticipated on a bond if it is held until the end of its lifetime.
Face Value
The nominal value printed on a financial instrument such as a bond or stock certificate; it is the amount paid at maturity or when the instrument is issued.
- Determine the bond pricing under assorted market dynamics, including the impact of interest rates and the period until maturity is reached.
- Outline the specifics of zero-coupon bonds and measure their financial value across diverse time points.
Verified Answer
ZD
Zherica DavisJul 13, 2024
Final Answer :
A
Explanation :
The price of a zero-coupon bond can be calculated using the formula: Price = Face Value / (1 + yield)^n, where n is the number of years to maturity. Given that the bond was purchased for $214.51 and matures in 20 years, we can find the yield to maturity by rearranging the formula: 214.51 = 1000 / (1 + yield)^20. Solving for the yield gives us a constant rate that applies throughout the bond's life. Five years later, the bond will have 15 years left to maturity. Using the same yield and the formula, we calculate the new price with n = 15. The correct answer, $315.20, reflects the bond's price increase as it gets closer to maturity, assuming the yield remains unchanged.
Learning Objectives
- Determine the bond pricing under assorted market dynamics, including the impact of interest rates and the period until maturity is reached.
- Outline the specifics of zero-coupon bonds and measure their financial value across diverse time points.