Consider a five-year (n = 10) "super-floater" where the semi-annual coupon rate equals (y1 is the semi-annual spot rate):

c = 2% + 4 y1.

Assume M = 100.

Construct a portfolio of plain-vanilla floaters (c = y1), fix-rate coupon bonds (c = c ), and zero-coupon bonds (c = 0), that replicates the cash flows of the super-floater. Assume a flat spot curve at y = 2% (semi-annual rate). Calculate the price of the super-floater and its modified duration.