A company faces a stream of obligations over the next $8$ years as shown: where the numbers denote thousands of dollars.

$\backslash$table$[[$Year$,1,2,3,4,5,6,7,8,9],[,60,80,100,120,100,80,60,40,20]]$

The spot rate curve is that of Example $4\mathrm{.}8$ in the textbook. Find a portfolio, consisting of the two bonds described in that example, that has the same present value as the obligation stream and is immunized against an additive shift in the spot rate curve.

TABLE $4\mathrm{.}4$

Worksheet for Immunization Problem

$\backslash$table$[[$Year$,$Spot,$d,B_1,P{V}_1,-P{V}_1^{\text{'}},B_2,P{V}_2,-P{V}_2^{\text{'}}$