An account credits interest in such a way that the monthly discount factor is constant, regardless of the month in which money is being discounted. Sue deposits $4000$ into the account exactly $1$ year after she made a deposit of $2000$ into the account. The $($total$)$ present value of Sue's deposits, one year before her first deposit, is $5510.$ Determine the annual accumulation factor for deposits into this account.

$)=(1\mathrm{.}05263$cdots