A firm issues a floater with 100 face value paying LIBOR every six months, two repricing and coupon payment dates are Jan 1 and July 1 each year. The floater will mature on Jan 1, 2044. Assume the yield curve is always flat. The floater was rated as AAA and has a similar credit quality as the LIBOR. 

a. On Jan 1, 2019, the effective annual interest rate was 7%. The floater can be decomposed into a zero coupon bond and a floating rate annuity. 

i. Find the price of the floater, the zero-coupon bond, and the annuity

ii. Find the duration and modified duration of the floater, the zero-coupon bond, and the annuity 

b. On March 1, 2019, the effective annual interest rate became 5%. The floater can be  regarded as a zero-coupon bond 

Find the time-to-maturity and face value of such zero coupon bond?

Find the price of the floater on March 1, 2019. Is it a premium or discount bond?

Find the approximate duration of the floater on March 1, 2019.