Two investments are made at the same time. The first consists of investing $1540$ dollars at an annual rate of interest of $9\mathrm{.}9$ percent, compounded semiannually. The second consists of investing $1400$ dollars at an annual rate of interest of $9\mathrm{.}9$ percent, compounded daily. How long will it take for the two investments to be worth exactly the same amount? $($Assume compound interest at all times.$)$

Answer $=$ years. $($Be sure to give several decimal places of accuracy!$)$