$($Term structure of interest rates$)$ You want to invest your savings of $$21,000$ in government securities for the next $2$ years. Currently, you can invest either in a security that pays interest of $8\mathrm{.}1\%$ per year for the next $2$ years or in a security that matures in $1$ year but pays only $5\mathrm{.}7\%$ 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 $1-$year security that pays an interest rate of only $5\mathrm{.}7\%,$ as opposed to investing in the $2-$year security paying $8\mathrm{.}1\%?$ 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 $11\mathrm{.}6\%$; otherwise, you will choose to go with the $2-$year security. What rationale could you offer for your preference?

a$.$ Why might you choose to make the investment in the $1-$year security that pays an interest rate of only $5\mathrm{.}7\%,$ as opposed to investing in the $2-$year security paying $8\mathrm{.}1\%?$ Provide numerical support for your answer. Which theory of term structure have you supported in your answer?

If you choose the $2-$year security, the value of your savings after the second year will be $$.($Round to the nearest dollar.$)$

If you choose to invest in the $1-$year security, the value of your savings after the first year will be $$.($Round to the nearest dollar.$)$

How much interest must the $1-$year security earn after its renewal in the second year in order for your account to equal the $2-$year investment?

To do as well as you would with the first choice, during the second year the $1-$year security would have to earn $ $($Round to the nearest dollar.$)$

In order for the investment in the $1-$year security to equal the $2-$year investment, how much should the renewal rate on the $1-$vear securitv be$?$