Answer:
The bond's yield to maturity is 9.45% using Excel to get exact values, and 9.59% using approximate method.
Explanation:
We can calculate is using 2 ways, using Excel to get the exact percentage or with approximate methods, calculating the semi-annual Yield to Maturity using the following formula
![YTM_{sm} =\cfrac{PMT+\cfrac{FV-PV}n}{\cfrac{FV+PV}2}](https://tex.z-dn.net/?f=YTM_%7Bsm%7D%20%3D%5Ccfrac%7BPMT%2B%5Ccfrac%7BFV-PV%7Dn%7D%7B%5Ccfrac%7BFV%2BPV%7D2%7D)
And from there we can calculate the Yield to Maturity just by multiplying the semi-annual one by 2.
Identifying the given information.
We have a period of 30 years, so for the semiannual bond we have
periods.
The face value, FV, is $1000, the coupon rate is 0.10, thus we can use them to find the interest per period PMT.
![PMT=0.10 \times \cfrac{1000}{2}\\PMT=\$ 50](https://tex.z-dn.net/?f=PMT%3D0.10%20%5Ctimes%20%5Ccfrac%7B1000%7D%7B2%7D%5C%5CPMT%3D%5C%24%2050)
The current price of the bond, PV is $1050.
Replacing the values on the semiannual Yield to Maturity
![YTM_{sm} =\cfrac{PMT+\cfrac{FV-PV}n}{\cfrac{FV+PV}2}](https://tex.z-dn.net/?f=YTM_%7Bsm%7D%20%3D%5Ccfrac%7BPMT%2B%5Ccfrac%7BFV-PV%7Dn%7D%7B%5Ccfrac%7BFV%2BPV%7D2%7D)
![YTM_{sm}=\cfrac{50+\cfrac{1000-1050}{60}}{\cfrac{1000+1050}{2}}](https://tex.z-dn.net/?f=YTM_%7Bsm%7D%3D%5Ccfrac%7B50%2B%5Ccfrac%7B1000-1050%7D%7B60%7D%7D%7B%5Ccfrac%7B1000%2B1050%7D%7B2%7D%7D)
Simplifying we get
![YTM_{sm}=4.797\%\\](https://tex.z-dn.net/?f=YTM_%7Bsm%7D%3D4.797%5C%25%5C%5C)
Finding the Yield to Maturity.
We can just multiply by 2 to get the Yield to Maturity from our previous result and rounding it to 2 decimals we get
![YTM = 2 YTM_{sm}\\YTM=9.59\%](https://tex.z-dn.net/?f=YTM%20%3D%202%20YTM_%7Bsm%7D%5C%5CYTM%3D9.59%5C%25)
Alternatively we can use Excel and write:
RATE(n, PMT, PV, FV)*2
That is
RATE(60,50,1050,1000)*2
And we will get the exact Yield to maturity 9.49%