Assume that we are given a set of forward rates for annual investments:

Using Eq. (3.47) we may directly find the corresponding spot rates:

It is interesting to notice that spot rates are increasing, even though the forward rates are not. We will discuss this matter further in Section 3.7.4.

Going the other way around requires a little more work, as it involves a triangular system of linear equations, much in the same vein as the bootstrapping procedure of Example 3.9.

Data From Equation  (3.47)

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f(0,0,1) = 2.0%, f(0,1,2) = 2.2%, f(0,2,3)=2.4%, f(0,3,4)= 2.3%.