Barry's Steroids Company has $1,000 par value bonds outstanding at 13 percent interest. The bonds will mature in 30 years.

If the percent yield to maturity is 11 percent, what percent of the total bond value does the repayment of principal represent? Assume interest payments are annual.

3.72%

Step-by-step explanation

the principal as a percentage of the bond price will be given by:

?principal as a percentage of the bond price=PV of BondPV of FV??

step 1: PV of FV

?PV=(1+r)nFV??

?PV=(1+11%)301000??

?PV=22.892296571000??

?PV =43.68281692?

step 2: PV of the bond:

the pv of the bond is calculated by:

?PV=C∗r1−(1+r)−n?+(1+r)nFV??

where:

C =coupn amount = 1000*13% =130

r= ytm =11%=0.11

n=period =30

substituting the values into the formula:

?PV=130∗0.111−(1+0.11)−30?+(1+0.11)301000??

?PV=130∗8.693792573+43.68281692?

?PV=1130.193035+43.68281692?

?PV =1,173.875851?

step 3: calculation of principal as a percentage of the bond price

?principal as a percentage of the bond price=PV of BondPV of FV??

?principal as a percentage of the bond price=1,173.87585143.68281692??

?principal as a percentage of the bond price=0.037212467?

?principal as a percentage of the bond price =3.72%?