Final answer:
To calculate the price of a 14-year zero-coupon bond with a 5.45% market interest rate and semiannual compounding, the present value formula is used. With a face value of $1,000, the computed price is approximately $490.39.
Step-by-step explanation:
To calculate the price of a zero-coupon bond that matures in 14 years with a market interest rate of 5.45 percent and semiannual compounding, we use the present value formula. The present value (PV) of a bond is determined by the formula PV = F / (1+r/n)^(nt), where F is the face value of the bond, r is the market interest rate, n is the number of compounding periods per year, and t is the number of years until maturity.
Assuming a face value (F) of $1,000 (as zero-coupon bonds typically have a face value of $1,000), a market interest rate (r) of 5.45 percent or 0.0545 in decimal form, semiannual compounding (n = 2), and maturity in 14 years (t = 14), we can calculate the bond's price as follows:
PV = 1000 / (1 + 0.0545/2)^(2*14) = 1000 / (1 + 0.02725)^(28)
Carrying out the calculations:
PV = 1000 / (1.02725)^(28)
PV = 1000 / 2.0391951
PV = $490.39
The price of the zero-coupon bond with the given parameters would be $490.39.