Answer:
Years until maturity date: 15
Explanation:
We need to solve for n.
The market value of the bond is the present value of the cuopon payment and the maturity date.
PV c + PV m = $1,012.7339
The present value of the annuity:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 60
time ?
rate 0.0587
[tex]60 \times \frac{1-(1+0.0587)^{-?} }{0.0587} = PV\\[/tex]
PVc
The present value of the face value at maturity date:
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time ?
rate 0.0587
[tex]\frac{1000}{(1 + 0.0587)^{?} } = PV[/tex]
PVm
[tex]\frac{1000}{(1 + 0.0587)^{?} } + 60 \times \frac{1-(1+0.0587)^{-?} }{0.0587}= 1012.73[/tex]
We can try to solve or do try and error
IF we use 10 as year until mature we got a market value of $1,009.6273
If we use 8 market value will be $1,008.1144
From this we got that we decrease 2 years and the market value decrease 1 dollar.
We can expect 1 dollar every 2 year.
at year 10 we have 1009 so to move to 1012 we increase 6 more years and recalculate
if N = 16 then Market value = $1,013.2558
we pass the market value, we decrease n 1 year
if n = 15 then market value = $1,012.7339
We got our given market value so 15 is the correct answer.
