5. (a) (8% In chapter 3 , we learnt that when we apply PCA to a set of interest rate data, the first three loading vectors often exhibit some interesting patterns. Please give a description of these patterns. And how these patterns agree with the structure of the Nelson-Siegel Model. (b) (6%) Please provide a numerical example to illustrate how we can apply the bootstrapping method learnt in chapter 3 to get zero rates from bond prices. (c) (6%) In chapter 7, we learnt two methods namely CPM and PERT. Please explain their differences in terms of methods and applications