Grandparents Annuity Your grandparents have an annuity. The value of the annuity increases

each month by an automatic deposit of $1\%$ interest on the previous month's balance.Your grand$-$

parents withdraw $2500$ at the beginning of each month for living expenses. Currently, they have

$125,000$ in the annuity. Model the annuity with a dynamical system. Will the annuity run out of

money? When? Hint: What value will $a_n$ have when the annuity is depleted?