Maturity$($years$)$

$1$

$2$

$3$

$4$

Coupon rate$($annual payments$)$

$0\mathrm{.}000\mathrm{.}00\%$

$10\mathrm{.}0010\mathrm{.}00\%$

$6\mathrm{.}006\mathrm{.}00\%$

$12\mathrm{.}0012\mathrm{.}00\%$

YTM

$2\mathrm{.}0002\mathrm{.}000\%$

$3\mathrm{.}9083\mathrm{.}908\%$

$5\mathrm{.}8405\mathrm{.}840\%$

$5\mathrm{.}7835\mathrm{.}783\%$

a$.$ Use arbitrage to determine the yield to maturity of a$$ two$-$year, zero$-$coupon bond.

b$.$ What is the$$ zero$-$coupon yield curve for years $1$ through$4?$

Note$$:

Assume annual compounding.