For a life annuity$-$due issued to $(55),$ you are given:

$(1)$ The annuity pays an annual benefit of $x$ through age $64$;

$(2)$ Beginning at age $65,$ the annuity pays $75\%$ of $x$;

$(3)$ The present value of this annuity is $250000$ ;

$(4)a_{55}^{}=16\mathrm{.}0599$;$,a_{55\text{:}101}^{}=8\mathrm{.}0192$;$,i=0\mathrm{.}05.$

Calculate $x.$