Suppose you have $$2,200$ and plan to purchase a $10-$year certificate of deposit $($CD$)$ that pays $13\mathrm{.}9\%$ interest, compounded annually. How much will you have when the CD matures?

a$.$ $$2,505\mathrm{.}80$

b$.$ $$8,084\mathrm{.}63$

c$.$ $$9,826\mathrm{.}33$

d$.$ $$7,098\mathrm{.}00$

e$.$ $$8,434\mathrm{.}09$

Suppose the real risk$-$free rate is $4\mathrm{.}00\%$ and the future rate of inflation is expected to be constant at $3\mathrm{.}10\%.$ What rate of return would you expect on a $1-$year Treasury security, assuming the pure expectations theory is valid? Include cross$-$product terms, i$.$e$.,$ if averaging is required, use the geometric average. $($Round your final answer to $2$ decimal places.$)$

a$.3\mathrm{.}22\%$

b$.7\mathrm{.}22\%$

c$.4\mathrm{.}00\%$

d$.7\mathrm{.}10\%$

e$.4\mathrm{.}12\%$