Please answer all parts

Question 2 3+3+5+4=15 marks You take out a home loan for $1,200,000. Payments need to be made monthly and interest is charged monthly, at a rate of 0.25% (that is, 3% per annum). (a) Letting a,, denote the amount owed after n months from taking out the loan, and assuming regular monthly payments of Sp, which start a month after the loan taking out, show that the amount owed can be modelled by the following recurrence relation, On+1 = 1.00250. - P. and also give the initial condition. (b) Determine the equilibrium value for the recurrence relation and interpret its meaning. Would the equilibrium value be stable or unstable? Note you are not being asked to prove if equilibrium is stable or unstable, but give some intuitive justification for your answer. (c) Solve the recurrence relation. (d) Given you decide to take out the loan for 30 years, what should the monthly payments p be