Find the accumulated value of an annuity of $$1000$ payable at the end of each month for a total of $10$ years. The interest rate is $6\%$ compounded monthly for the first $5$ years and $7\%$ compounded monthly for the last $5$ years.

$71587\mathrm{.}90$

$120000\mathrm{.}00$

$235328\mathrm{.}87$

$170500\mathrm{.}66$