A wise pensioner has invested in an annuity investment in one of South Africa's leading authorised financial services provider. The value of the annuity increases each month by an automatic deposit of 1% interest on the previous month's balance. The pensioner withdraws R4000 each month for groceries and other expenses. Currently, the pensioner has R350 000 in the annuity. Let P represent the funds in the annuity at the end of the month n, with P, being the initial principal amount. (5.1) Write down the model for the annuity investment. (5.2) Determine the equilibrium point(s) of the model, if they do not exist justify your solution. (5.3) Utilize formulation to determine as to when will the annuity be depleted.