On his $30$th birthday $(t=30),$ Julio begins saving his money for retirement. He puts

$1000$ into an account earning $2\%$ interest. He gets a raise most years, so will add $100$ to

each subsequent payment $($when $t=31,$ the payment is $1100,t=32,$ payment equals

$.$ He makes his last deposit on his $65$th birthday. He immediately purchases a

$25-$year annuity immediate, with a first payment of $x$ and each additional payment

increasing by $2\%.$ The price of the annuity was calculated using $i=0\mathrm{.}02.$ Calculate

X$.[5384\mathrm{.}22]$