A grandmother offers her granddaughter Jennifer two choices for a saving plan: Option 1: On 31 December of year 1, the grandmother opens a bank account with 130$ for Jennifer. Starting in year 2, she deposits 170$ into this account on 1 January of every year On 31 December of each year (excluding year 1), she pays 'interest', that is, she deposits an amount that corresponds to 6% of the account balance on that day to the account. Let B(n) denote the amount of money i n the account on 31 December of vear n Option 2: On 31 December of year 1, the grandmother opens a bank account with 180 for Jennifer. On 31 December of each year (excluding year 1), she pays 'interest', that is, she deposits an amount that corresponds to 2.9% of the account balance on that day into the account. Immediately after the 'interest payment', she deposits an additional 170S to the account. Let A(n) denote the amount of money in the account on 31 December of year n (a) Find a recursive definition for An. (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 to compute An and Bn forn- 1,2,...,10, and display the values in three columns: n, An, Bn with appropriate headings. Include a printout of the output with your solution. (d) Use MATLAB to create a plot showing A and B as a function of n for years 1 to 10. Label priately. Include a printout of the plot with your solution. (e) If the saving scheme runs for 7 years, should Jennifer choose the first or the second option your axes appro (in order to maximise the account balance at the end of the scheme)