a)The short rate of the nth year rn should be equal to the forward rate of the nth year fn
So, the forward rate for the nth year fn is given by
(1+yn)n = (1+yn-1)n-1*(1+fn)
So, (1+fn) = (1+yn)n / (1+yn-1)n-1
which is the required formula
b) y2 the yield rate for two years is dependent upon r1 and r2
where r1 is the rate for one year and r2 is the rate from 1st year to 2nd year
So, (1+y2)2 = (1+r1) * (1+E(r2))
=> (1+y2)2 = (1+0.05)*(1+0.06) =1.113
=> (1+y2) = sqrt (1.113) = 1.054988
=> y2 = 0.054988 = 5.499%
c) If y2 = 6.49%, r1=5%
So, we have (1+y2)2 = (1+r1) * (1+f2)
=> (1+0.0649)2 = (1+0.05)* (1+f2)
=> (1+f2) = (1+0.0649)2 /(1+0.05) =1.080011
=> f2 = 0.080011 =8.00%
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