$2.$ Suppose you are given the following features of Bonds D$,$ E$,$ and F$.$

Price Yield Coupon rate Face Maturity

Bond D $$925\mathrm{.}5614\mathrm{.}673\%6\mathrm{.}400\%$ $$1,0001$

Bond E $$930\mathrm{.}4414\mathrm{.}417\%6\mathrm{.}700\%$ $$1,0001$

Bond F $$933\mathrm{.}5014\mathrm{.}270\%6\mathrm{.}900\%$ $$1,0001$

$2$a$.$ What is the arbitrage$-$free six$-$month spot rate?

$2$b$.$ What is the arbitrage$-$free one$-$year spot rate?

$2$c$.$ What is the arbitrage$-$free price of Bond F$?$