For an apartment mortgage finance system, let 𝑦[𝑛] be total money owed to the bank at the month of n, wi

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For an apartment mortgage finance system, let 𝑦[𝑛] be total money owed to the bank at the month of n, with 𝑦[0] is the total amount of the credit financed. Let the monthly interest rate be fixed at 𝛼%. The amount of the monthly fixed payment one makes may be considered as the input changing the total dept amount at any given month, 𝑥[𝑛] = 𝑋(constant for all n) for the 𝑛𝑡h month payment. The total number of payments needed to pay off the debt is 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 1,000,000 TL to purchase an apartment
at 𝛼 = 1% monthly rate for 10 years, what would be the monthly installment 𝑋?
d) Now, assume that you can only afford to pay 20,000 TL/month max. How long you must make
payments to clear the dept?
e) Find out a fair rent value of the property that that will not change the total loan amount as if
it were paid to the bank monthly. (Don’t forget to add 20% taxes and fees).