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

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

Develop the precise recurrence relation that characterizes this financial scenario.

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.

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