Question 6: 16 Marks 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 An additional deposit of AV is added to the account at the end of each month, and the fixed amount R 500 is withdrawn from the account. Let A, represent the amount of money in the account at the end of the month n, with A, denoting the original amount. (6.1) Write down the difference equation for A, (that is, an expression for A,, in terms of A,). Write down also, the initial value, A- (6.2) How should the value NV be chosen such that there will always be money in the account? Justify your answer! APM1514/101/0/2022 Question 7: 20 Marks 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 R:500 is made at the beginning of each month. Let A, denote the amount of money still owing at the end of month a, with A, denoting the original loan amount. (7.1) Write down the difference equation for 4, (that is, an expression for 4., in terms of A,). (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 0ou. (b) Change the repayment to Rio01) per month. (c) Change the interest rate to 37 per month