Question

What is the yield to maturity (YTM) of a zero coupon bond with a face value of $1,000, current price of $920 and maturity of 3.5 years? Recall that the compounding interval is 6 months and the YTM, like all interest rates, is reported on an annualized basis. (Allow two decimals in the percentage but do not enter the % sign.)

Answer 1

value of zero coupon bond = face value / (1+r)^n

here,

value of bond = $922

face value = $1,000.

r= to be found out.

n =3.5 years * 2 semi annual periods

=>7 years.

$922 = $1000/(1+r)^7

=>(1+r)^7 = 1000/922

=>(1+r)^7 = 1.084599.

=> (1+r) = (1.084599)^(1/7)

=>1+r =1.01166899

=>1+r = 0.01166899

=>r=1.17%. for six months

annualised rate = 1.17% *2

=>3.34%.