Answer:
years to maturity:
Explanation:
The market value will be the present value of the bons at 9.34% YTM
Present value of the cuopon payment will be an aordinary annuity:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 40 (1,000 x 8%/2 payment per year
time n (unknow value)
rate 0.0934
[tex]40 \times \frac{1-(1+0.0467)^{-n} }{0.0467} = PV_c\\[/tex]
Present value of the maturity, which is present value of a lump sum
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex] Â
Maturity  1,000.00
time  n
rate  0.0467 (rate / 2 as there are 2 payment per year)
[tex]\frac{1000}{(1 + 0.0467)^{n} } = PV_m[/tex] Â
We know that:
PVc + PVm = Market price = 889.83
So we can build this equation:
[tex]40 \times \frac{1-(1+0.0467)^{-n} }{0.0467} + \frac{1000}{(1 + 0.0467)^{n} } Â = 889.83\\[/tex]
Based on the values we are given, we solve for "n"
First, we work out the annuit y formula:
[tex] \frac{40}{0.0467} - Â \frac{40}{0.0467\times1.0467^n+ \frac{1000}{(1 + 0.0467)^{n} } Â = 889.83\\[/tex]
Then we do common factor:
[tex] 1.0467^{-n} \times ( 1000 - \frac{40}{0.0467}) = 889.83 - \frac{40}{0.0467} Â \\[/tex]
We solve and leave this:
[tex] 1.0467^{-n} Â \times 143,689507 = 33.29895075[/tex]
[tex] 1.0467^{-n} Â = 0.232098657[/tex]
We now apply logarthimic properties to sovle for n
[tex] -n  = \frac{log 0.232098657}{log  1.0467}[/tex]
n = 32 These are semiannual payment, so we divide by 2 to convert to year:
32/2 = 16 years
