8- The following term structure is given as effective annual rates of interest on zero coupon bonds:

1-year maturity: 6%, 2-year maturity: 7%, 3-year maturity: 9%.

(a) Find the 1-year forward effective annual interest rate for a 1-year period, [1,2]f[1,2] and find the 2-year forward effective annual interest rate for a 1-year period, [2,3]f[2,3].

(b) The effective annual rate of interest for a 4-year zero coupon bond is 4r4. Find the minimum value of 4r4 needed so that [3,4][2,3]f[3,4]f[2,3], where [3,4]f[3,4] is the 3-year forward effective annual interest rate for a 1-year period and [2,3]f[2,3] is found in part (a).