Consider a cheque account. Initially, the amount of R 10 000 is deposited into the account. At the end of each month, interest is added at the rate of 2% per month to the amount of money that was in the account during the month. An additional deposit of N is added to the account at the end of each month, and the fixed amount R 500 is withdrawn from the account. Let An represent the amount of money in the account at the end of the month n, with Ao denoting the original amount. (6.1) Write down the difference equation for An (that is, an expression for An+1 in terms of An). Write down also, the initial value, A. (6.2) How should the value N be chosen such that there will always be money in the account? Justify your answer! Consider a house loan of R300 000, on which interest is charged at the rate of 1.5% per month at the end of the month; and a repayment of R3500 is made at the beginning of each month. Let An denote the amount of money still owing at the end of month n, with Ao denoting the original loan amount. (7.1) Write down the difference equation for An (that is, an expression for An+1 in terms of An). (7.2) Find the equilibrium point of the system. (7.3) Will the house loan eventually be paid off or not? Justify your answer! (7.4) Does the difference equation in (a) change (and if it does, how), if the following change is made to the situation: (a) Make the initial loan amount R500 000. (b) Change the repayment to R1600 per month. (c) Change the interest rate to 3% per month.