Clair purchases a $12-$year, zero$-$coupon bond that matures for $2850.$ The bond is priced to yield $3\mathrm{.}5\%$ annual effective. Clair sells the bond to Lucas $7$ years after she purchased it$.$ The price paid by Lucas will yield him an annual effective return of $4\mathrm{.}2\%.$ Calculate the annual effective yield actually earned by Clair.