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Homework answers / question archive / A bond pays annual coupons at a rate of 5

A bond pays annual coupons at a rate of 5

Finance

A bond pays annual coupons at a rate of 5.5%. Its face value is $1000. The bond has exactly 3 years until it matures. The price of the bond is 1040.31. If the two - and three year spot rates in this economy are 5% and 4%, then the one year spot rate is closest to?
Select one:
a. 1.05%
b. 5.5%
c. 4.48%
d. 4.70%

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Answer is d.

This question is of term structuring of bond.

Therefore the equation will be

1040.31=[interest/(1+r)] + [interest/(1+r)2]+[interest+principal/(1+r)3]

Therefore,1040.31=[55/(1+r)]+[55/(1.05)2]+[1055/(1.04)3]

= 1040.31=[55/(1+r)]+49.89+937.89

= 1040.31-49.89-937.89=55/(1+r)

= 52.53=55/(1+r)

      = r= [(55/52.53)-1]×100

  = r=4.70%

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