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2. [13 marks] Consider the following two saving schemes. Option 1: On 31 December of year 0, a grandmother opens a bank account with 1,700$ for her daughter. On 31 December of each year (excluding year 0), she pays 'interest, that is, she deposits an amount that corresponds to 2.5% of the account balance on that day into the account. Further, in each year (excluding year 0), immediately after the 'interest payment on 31 December, she deposits an additional 130$ to the account. Let A, denote the amount of money in the account on 31 December of year n (after interest payment and deposit). Option 2: On 31 December of year (), a grandmother opens a bank account with 1,700$ for her granddaughter. Starting in year 1, she deposits 125$ into this account on 1 January of every year. On 31 December of each year (excluding year 0), she pays 'interest, that is, hishe deposits an amount that corresponds to 2.5% of the account balance on that day to the account. Let B, denote the amount of money in the account on 31 December of year n (at close of business, that is, after the interest was paid). 1 (a) Find a recursive definition for A.. (You may find it helpful to draw a timeline.) (b) Find a recursive definition for B,. (You may find it helpful to draw a timeline.) (C) Write a MATLAB program that computes A, and B, for n = 0,1,2,..., 12, and that displays the values in three columns: n, A., B, with appropriate headings. Include a printout of the output with your solution, (d) Use MATLAB to create a plot showing 1, and B, as a function of n for years 1 to 12. Label your axes appropriately. Include a printout of the plot with your solution. (e) Adapt your MATLAB program so that it computes how much total interest is accrued for cach of the two schemes in the years a 12, and what the average amount of interest is that is paid for each scheme per year over the years. 12. Provide the average amount of yearly interest for each of the two schemes. 2. [13 marks] Consider the following two saving schemes. Option 1: On 31 December of year 0, a grandmother opens a bank account with 1,700$ for her daughter. On 31 December of each year (excluding year 0), she pays 'interest, that is, she deposits an amount that corresponds to 2.5% of the account balance on that day into the account. Further, in each year (excluding year 0), immediately after the 'interest payment on 31 December, she deposits an additional 130$ to the account. Let A, denote the amount of money in the account on 31 December of year n (after interest payment and deposit). Option 2: On 31 December of year (), a grandmother opens a bank account with 1,700$ for her granddaughter. Starting in year 1, she deposits 125$ into this account on 1 January of every year. On 31 December of each year (excluding year 0), she pays 'interest, that is, hishe deposits an amount that corresponds to 2.5% of the account balance on that day to the account. Let B, denote the amount of money in the account on 31 December of year n (at close of business, that is, after the interest was paid). 1 (a) Find a recursive definition for A.. (You may find it helpful to draw a timeline.) (b) Find a recursive definition for B,. (You may find it helpful to draw a timeline.) (C) Write a MATLAB program that computes A, and B, for n = 0,1,2,..., 12, and that displays the values in three columns: n, A., B, with appropriate headings. Include a printout of the output with your solution, (d) Use MATLAB to create a plot showing 1, and B, as a function of n for years 1 to 12. Label your axes appropriately. Include a printout of the plot with your solution. (e) Adapt your MATLAB program so that it computes how much total interest is accrued for cach of the two schemes in the years a 12, and what the average amount of interest is that is paid for each scheme per year over the years. 12. Provide the average amount of yearly interest for each of the two schemes