Answer:
at 13% --> $1,000
at 17% -->$806.54
at 10% --> $1,194.85
When the rates do not match people will only accept the bond if their desired market return can be acheive. Because, the coupon payment are fixed the only way to do so is by changing the price ofthe bond.
So bond with coupon rate above market are trade at a price higher than face value while, below market traded at lower price.
Explanation:
The market value of a bond is the present value of the future coupon payment and maturity given the current market rate
When the market rate matches the coupon rate then the bond is at par and sales at face value.
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 130.000
time 11
rate 0.17
[tex]130 \times \frac{1-(1+0.17)^{-11} }{0.17} = PV\\[/tex]
PV $628.7337
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 11.00
rate 0.17
[tex]\frac{1000}{(1 + 0.17)^{11} } = PV[/tex]
PV 177.81
PV c $628.7337
PV m $177.8097
Total $806.5435
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 130.000
time 11
rate 0.1
[tex]130 \times \frac{1-(1+0.1)^{-11} }{0.1} = PV\\[/tex]
PV $844.3579
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 11.00
rate 0.1
[tex]\frac{1000}{(1 + 0.1)^{11} } = PV[/tex]
PV 350.49
PV c $844.3579
PV m $350.4939
Total $1,194.8518
