Answer:
YTM: 2.64%
YTC: 3.66%
Explanation:
The market price is the discounted price of the maturity and coupon payment at market rate:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 3.700
time 40
rate 0.013221404
[tex]3.7 \times \frac{1-(1+0.0132214040405666)^{-40} }{0.0132214040405666} = PV\\[/tex]
PV $114.3676
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 100.00
time 40.00
rate 0.013221404
[tex]\frac{100}{(1 + 0.0132214040405666)^{40} } = PV[/tex]
PV 59.13
PV c $114.3676
PV m $59.1324
Total $173.5000
Then we do the same calcaulation with the 161 call price being the maturity and adjusting time for 10 years (20 payment)
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 3.700
time 20
rate 0.018309924
[tex]3.7 \times \frac{1-(1+0.0183099243918235)^{-20} }{0.0183099243918235} = PV\\[/tex]
PV $61.4988
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 161.00
time 20.00
rate 0.018309924
[tex]\frac{161}{(1 + 0.0183099243918235)^{20} } = PV[/tex]
PV 112.00
PV c $61.4988
PV m $112.0021
Total $173.5009
Now we got the semiannual rate we simply multiply by two to convert into annual rates.
YTM:
0.013221404 X 2 = 0,026442808 = 2.64%
YTC:
0.0183099243918235 X 2 = 0,036619848783647 = 0.0366 = 3.66%
