Answer:
The bond will yield 3.8% as their yield to maturity did not change. Below is the calculation to check it.
Explanation:
As the bond market price change over time, there is a capital gain/loss we need to figure it out.
We solve for the market price of the bond 5-year before and 4 years before maturity:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 58.000
time 5
rate 0.038
[tex]58 \times \frac{1-(1+0.038)^{-5} }{0.038} = PV\\[/tex]
PV $259.6629
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 5.00
rate 0.038
[tex]\frac{1000}{(1 + 0.038)^{5} } = PV[/tex]
PV 829.88
PV c $259.6629
PV m $829.8761
Total $1,089.5389
Now, 4-years:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 58.000
time 4
rate 0.038
[tex]58 \times \frac{1-(1+0.038)^{-4} }{0.038} = PV\\[/tex]
PV $211.5301
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 4.00
rate 0.038
[tex]\frac{1000}{(1 + 0.038)^{4} } = PV[/tex]
PV 861.41
PV c $211.5301
PV m $861.4113
Total $1,072.9414
the return will be:
(interest + capital result ) / investment
(interest + 4-year price - 5-year price) / investment
(58 + 1,072.94 - 1,089.54) / 1,089.54 = 0.037997687
