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There is a zero coupon bond that sells for $351.98 and has a par value of $1,000. If the bond has 20 years to maturity, what is the yield to maturity? Assume semiannual compounding.

a- 5.16%
b- 5.08%
c- 5.11%
d-5.36%
e- 5.29%

User Maembe
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1 Answer

5 votes

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%%.

User Chikak
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