A $10-$year $8\%$ coupon bond currently sells for $$90.$ A $10-$year $4\%$ coupon bond currently sells for $$80.$ What is the $10-$year zero rate? Use continuous compounding.

If your answer is $4\mathrm{.}56789\%,$ write it as $0\mathrm{.}0457(4$ digits, $0.)$