A fairly priced 3-year $100 par value 5% coupon rate payable semiannually bond has a YTM of 5.365321% (BEY). The short-term forward-rate curve (i.e., 1fm for m = 0, 1, 2, 3, 4, and 5) on a BEY basis is: 3%, 3.2%, 3.6%, 4.2%, 5%, and X%, respectively. What is X?

Consider the following two 3-year Treasury notes that have the same par value (the exact par value is irrelevant here, but the par value is not equal to either $100 or $1,000): a 3% coupon payable semi-annually note selling at $93 and a 9% coupon paid every six months note trading at $109. 

Using these two notes, you are able to synthesize a 3-year Treasury zero-coupon bond of the same par value. 

What is the price of this zero-coupon bond?