A (yearly) cash flow stream is $\mathbf{x}=(-40,10,10,10,10,10,10)$. The spot rates are those of Exercise 2.

(a) Find the current discount factors $d_{0, k}$ and use them to determine the (net) present value of the stream.

(b) Find the series of expectations dynamics short-rate discount factors, and use the running present value method to evaluate the stream.

Data from Exercise 2

Given the (yearly) spot rate curve $s=(5.0,5.3,5.6,5.8,6.0,6.1)$, find the spot rate curve for next year.