There is a zero coupon bond that sells for $4,550.90 and has a par value of $10,000. If the bond has 18 years to maturity, what is the yield to maturity'? Assume semiannual compounding. A. 4.47%
B. 4.27%
C. 4.31%
D. 4.24%
E. 4.42%

E. 4.42%

Explanation:

Calculation for the yield to maturity

First step is to calculate the Current price using this formula

The Current price=Par value/(1+yield to maturity/2)^(2*Time period)

$4,550.90=$10,000/(1+yield to maturity/2)^(2*18)

(1+yield to maturity/2)^36=($10,000/$4,550.90)

1+yield to maturity/2=($10,000/$4,550.90)^(1/36)

Now let calculate the yield to maturity

Yield to maturity/2=1.0221092-1

Yield to maturity=0.0221092*2

Yield to maturity=0.0442*100

Yield to maturity=4.42%

Therefore the Yield to maturity will be 4.42%

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