I'm having trouble understanding how to calculate the yield of maturity of a bond.

Here is an excerpt from my textbook.

Then it has them solutions listed belowSuppose that the current term structure has the following yields on zero coupon bonds

Term ___________ Zero Coupon Bond Rate

1/2 Year______________8%

1 Year________________9%

1 1/2 Year____________10%

2 Year________________11%

Find the price per $100 face amount and yield to maturity of each of the following 2-year bonds (with semi-annual coupons):

(i) zero coupon bond

(ii) 5% annual coupon rate

(iii) 10% annual coupon rate

I understand how they calculated the price, but I have look throughout my whole notes and the book and it never explains how they calculated the yield to maturity.(i) Price is 100(1+.055)^-4= 80.72 and yield to maturity is (nominal) 11%

(ii) Price is 2.5[(1.04)^-1+(1.045)^-2+(1.05)^-3]+102.5(1.055)^-4= 89.59

Yield to maturity is (nominal) 10.9354%

(iii) Price is 5[(1.04)^-1+(1.045)^-2+(1.05)^-3]+105(1.055)^-4= 98.46

Yield to maturity is (nominal) 10.8775%

If anyone knows how, i would highly appreciate it, final exam is tomorrow!