Please explain in detail how you solved this question, thank you.

Charles has worked very hard through his career as a teacher and is contemplating an early retirement. He already has a pension in place commencing at retirement age but wants to cut back on his teaching duties immediately. To supplement his income, Charles has a retirement savings plan which will allow him to make withdrawals from a savings account from 10 years prior to the retirement age. Charles needs to work out the minimum amount required in the savings account with the following specifications. - Interest Credit - Interest on Savings will be paid at a rate of 5\% p.a. - Withdrawals - starting with $10000 at the end of the first year growing by 3% each year (end) to cater for inflation. - The savings account will be depleted at the end of the 10 years (nil balance). Let St to be the minimum required savings account balance at time t. ( t=0 represents today, t=10 represents the time of retirement). (a) Explain why the following equation is a suitable finite difference model for this scenario: St+1=1.05St100001.03t (b) Considering the savings account will be depleted at the end of the 10 years, what is a suitable boundary condition that will be used to find a solution to this problem? (c) Calculate the complementary function for this retirement savings plan. (d) Because the term 100001.03t in Equation (1) is a function in t and not a constant, an adjustment needs to be made. Divide Equation (1) throughout by 1.03t and redefine a new variable Yt=1.03tSt Rewrite Equation (1) again in the form of Yt+1=AYt+B (1a) for suitable A and B values. (e) Compute the particular solution for Equation (1a), first in terms of Yt but ultimately in terms of St for the solution to Equation (1). (f) Calculate S0, the amount of money needed today to finance Charles' pre-retirement plan