In a particular bond market, the two$-$year par yield at time t $=0$ is $4\mathrm{.}15\%$ and the issue price at

time t$=0$ of a two$-$year fixed interest stock, paying coupons of $8\%$ annually in arrears and redeemed at $98,$ is $$105\mathrm{.}40$ per $$100$ nominal. Calculate:

$($a$)$ the one$-$year spot rate

$($b$)$ the two$-$year spot rate