Consider an annuity with an initial value of R78000 and monthly withdrawals of Ry. The annuity has an interest rate of 4% per annum, compounded monthly.

1. Develop the precise recurrence relation that characterizes this financial scenario.

2. Construct a model for the remaining value in the annuity after n months and determine the value of the monthly withdrawals, such the remaining balance in the annuity after a period of 9 months is R45000. Show all workings