Final answer:
The correct answer is b .The yield to maturity (YTM) of the zero coupon bond given is approximately 5.08%, which is calculated using the formula for YTM with semiannual compounding and then annualizing the result.
Step-by-step explanation:
To calculate the yield to maturity (YTM) of a zero coupon bond with semiannual compounding, you can use the following formula:
YTM = √[FV / PV]^(1/n) - 1
Where FV is the face value of the bond, PV is the present value (price) of the bond, and n is the number of periods to maturity.
In this case, FV = $1,000, PV = $351.98, and n = 40 (20 years * 2, since it's semiannual). Plugging these values into the formula:
YTM = √[$1,000 / $351.98]^(1/40) - 1
After calculating, the YTM on a semiannual basis comes to roughly 2.54%. To annualize this (since YTM is typically expressed annually), we multiply by 2:
Annual YTM = 2.54% * 2 = 5.08%
Therefore, the correct answer is (b) 5.08%%.