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For an apartment mortgage finance system, let y[n] be total money owed to the bank with y[0] is the total amount of the financed part of the property. Let the monthly interest rate be fixed a. The amount of the monthly fixed payment one makes is x[n] = X for the nth month payment. Total number of payments be N. a) Write the difference equation modeling this finance system with payment X being the input and total amount of debt as the output. b) Find the solution of y[n] c) Use the solution to calculate if one needs to finance 500,000 TL to purchase the house at a = 0.79% monthly financing rate in 10 years (N=120), what would be the monthly installment X? For an apartment mortgage finance system, let y[n] be total money owed to the bank with y[0] is the total amount of the financed part of the property. Let the monthly interest rate be fixed a. The amount of the monthly fixed payment one makes is x[n] = X for the nth month payment. Total number of payments be N. a) Write the difference equation modeling this finance system with payment X being the input and total amount of debt as the output. b) Find the solution of y[n] c) Use the solution to calculate if one needs to finance 500,000 TL to purchase the house at a = 0.79% monthly financing rate in 10 years (N=120), what would be the monthly installment X