Suppose that you need $$35,000$ in three years and that you can

finance this with zero$-$coupon bonds yielding $5\mathrm{.}5\%$ in terms of two

years and six years. Imagine that you spend $$22,354\mathrm{.}86$ purchasing a

$2$ year bond$$7451\mathrm{.}62$ for a six$-$year$$bond$,$ and these are each

priced yield $5\mathrm{.}5\%.$ Suppose also that at the end of two years, no

matter what the yield rate i may then be$,$ you sell the remaining

bond at a purchase price to yield i$,$ combine the proceeds with

$$24,881\mathrm{.}52$ from the redeemed bond, and use the total to buy a

one$-$year zero$-$coupon$$bond$.$ Illustrate that this immunizes

against interest rate risk by showing that it produces the needed

$$35,000$ three years after your initial bond purchases if i$=18\%($a

high rate$)$ or i$=1\%($a low rate$).$