Answer:
Yield price at year-end $746.55
taxable income: capital gain + coupon payment
16.55 + 60 = $76.55
Explanation:
First we solve for the yield, which is the rate at which the discounted maturity and bond coupon payment matches the market price:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 60.000
time 10
rate 0.104863443
[tex]60 \times \frac{1-(1+0.104863442947447)^{-10} }{0.104863442947447} = PV\\[/tex]
PV $361.0956
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 10.00
rate 0.104863443
[tex]\frac{1000}{(1 + 0.104863442947447)^{10} } = PV[/tex]
PV 368.90
PV c $361.0956
PV m $368.9045
Total $730.0001
So the market rate is 10.49%
Now we solve for the value of the bond at year-end:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 60.000
time 9
rate 0.104863443
[tex]60 \times \frac{1-(1+0.104863442947447)^{-9} }{0.104863442947447} = PV\\[/tex]
PV $338.9613
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 9.00
rate 0.104863443
[tex]\frac{1000}{(1 + 0.104863442947447)^{9} } = PV[/tex]
PV 407.59
PV c $ 338.96
PV m $ 407.59
Total $ 746.55
