Answer:
7.32%
Explanation:
The price of a bond is the present of its interest payment and the present value of redemption value (RV
Present value of the Redemption Value (RV) =
FV× (1+r/2)^(-2×n)
FV- 2000, r- yield rate, r/2= 6.74%/2 = 3.37%, n-22
=2000× (1.0337)^(-2×22)
= 465.233
Present Value of the coupon payment =Price of bond - PV of RV
= (106.657% × 2000) - 465.233
= $1667.90
PV of coupon payment= A × (1-(1+r)^(-2×n)
A- semiannual coupon payment, r -yield
1667.90 = A × (1-(1.0337)^(-2*22))/0.0337
1,667.90 = A × 22.7710
A = 1,667.90/22.7710
A= 73.246
Annual coupon payment = 2× 73.246= 146.493
Annual coupon rate = coupon payment/ face value
= (146.493/2,000 )× 100
= 7.32%
Answer:
Coupon rate is 7.32%
Explanation:
In calculating the coupon rate on the bond,we first of all need to determine the amount of interest payable by the bond on semi-annual basis using the pmt formula in excel:
=pmt(rate,nper,-pv,fv)
rate is the yield to maturity divided by 2 since it is a semi-annual interest paying bond i.e 6.74%/2
nper is the time to maturity of the bond multiplied by 2=22*2=44
the present value is the current price of the bond:$2000*106.657%=$2133.14
The fv is the face value of $2000
=pmt(6.74%/2,44,-2133.14 ,2000)
pmt= 73.25
annual pmt= 73.25*2= 146.49
coupon rate=pmt/face value= 146.49/2000
=7.32%
