Answer :
Answer:
The bonds price is $1,047.71
Explanation:
The present value of a bond will be the coupon payment and maturity discounted at the current market rate.
We assume the bonds face value is 1,000 dollars.
The coupon payment wil be an ordinary annuity:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C: 1,000 x 10%/2 payment per year = $50
time 10 (5 years x 2 payment per year)
rate 0.044 (8.8% annual / 2 = 4.4% semiannual)
[tex]50 \times \frac{1-(1+0.044)^{-10} }{0.044} = PV\\[/tex]
PV $397.5884
Then, maturity will be the present value of a lump sum
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 10.00
rate 0.044
[tex]\frac{1000}{(1 + 0.044)^{10} } = PV[/tex]
PV 650.12
We add both together and get:
PV of coupon payment + PV of maturity:
$397.5884 + $650.1222 = $1,047.7106