$($Term structure of interest rates$)$ You want to invest your savings of $$$$22$ comma $00022,000$ in government securities for the next $22$ years.$$ Currently, you can invest either in a security that pays interest of $8\mathrm{.}28\mathrm{.}2\%$ per year for the next $22$ years or in a security that matures in $11$ year but pays only $5\mathrm{.}95\mathrm{.}9\%$ interest. If you make the latter$$ choice, you would then reinvest your savings at the end of the first year for another year.

a$.$ Why might you choose to make the investment in the $11-$year security that pays an interest rate of only $5\mathrm{.}95\mathrm{.}9\%,$ as opposed to investing in the $22-$year security paying $8\mathrm{.}28\mathrm{.}2\%?$ Provide numerical support for your answer. Which theory of term structure have you supported in your$$ answer?

b$.$ Assume your required rate of return on the$$ second$-$year investment is $11\mathrm{.}611\mathrm{.}6\%$; $$otherwise$,$ you will choose to go with the $2$ dash year$2-$year security. What rationale could you offer for your$$ preference?