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%.
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