QUESTION
Your grandparents have an annuity. The value of the annuity increases each month as $1 \%$ interest on the previous month's balance is deposited. Your grandparents withdraw $\$ 1000$ each month for living expenses. Currently, they have $\$ 50,000$ in the annuity. Model the annuity with a dynamical system. Find the equilibrium value. What does the equilibrium value represent for this problem? Build a numerical solution to determine when the annuity is depleted.
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