$2-$year investment using two consecutive $1-$year $$500000$ zero coupon bonds is made. The maturity proceeds of the first zero coupon bond will be rolled over into the second zero coupon bond. The purchase yields for the two $1-$year zero coupon bonds will be $2\mathrm{.}03\%$ p$.$a$.$ and $3\mathrm{.}6\%$ p$.$a$.,$ respectively $($annual effective rates$).$ Note that any surplus funds after one year can be invested for one year at a rate of $3\mathrm{.}86\%$ p$.$a$.$

What annual effective percentage rate of compound interest will Narges earn

on this $2-$year investment? Round your results to three decimal places. a$.2\mathrm{.}816\%$ p$.$a$.$

b$.2\mathrm{.}830\%$ p$.$a$.$

c$.2\mathrm{.}844\%$ p$.$a$.$

d$.2\mathrm{.}858\%$ p$.$a$.$

e$.$ None of the above