Thank you for the opportunity to help you with your question!

the purchase price of the bond is $100

we need to identify the face value of the bond which is referred to as "par value"

find the remaining years to maturity. If the bond is maturing in 2020 and we are currently in 2015, then the bond matures in 5 years time

identify the annual interest of the bond in dollars. if the annual interest rate is 10% and the par value of the bond is $100 then the annual interest is 10% x $100 or $10.

calculating yield to maturity

100$-90$=10$

100/5=20

50+20=70

70/90=7.78%

100-20=80

70/98=7.14%

(7-78-7.14)/2=7.46%

so the yield to maturity is 7.46%

Please let me know if you need any clarification. I'm always happy to answer your questions.