Please answer all in MATLAB Format. Thanks!

2) Suppose one invests S500 per month for 5 years. If the desired total amount after 5 years were S60,000, then the required annual interest rate Icould be determined by the following equation: 60 500 I/12 -1 60,000 12 a) First, rewrite the equation in the form fu-0, where f(I) is a polynomial. i.e., in the form 50 12 where a, b, and c are appropriate constants. b) Next, use your answer from part (a) to compute f(iI) c) Write and run a script m-file, called newtl.m that performs Newton's Method. Use this script to find an estimate for I Your script will call two function m-files, fiewtmand fpnewt.m which are the function f(I) and its derivative, f(I), which you found in parts (a) and (b). Use initial guess 2, and run the loop until the relative error estimate XX for the latest root estimate, x. is less than a tolerance (TOL)of 105. Store all iterates in a vector, and display this vector as a column. d) Now, modify newtlmto a new script, newt2.m by adding lines to compute the ratios ee and e(e-") for each iteration. Use your final estimate from part (a) (all 16 digits) for the exact root in the errors. Store each of these ratios in 2 vectors and display the ratios for all1 as column vectors. Use the same initial guess x Do these ratios indicate whether this is a simple or multiple root? If so, state which one and why What are the estimated rate and order of convergence for the root? Page 3 of 4 e) Using only the first 3 significant digits of your final root estimate from part (c), apply the derivative definition of multiplicity to detemine whether or not this is a simple root. Does this confim your results from part (d)? f) Once you have determined the multiplicity of the root, compute the rate of convergence using the theoretical expression for the rate discussed in class. Again, use only the first 3 significant digits of your final root estimate from part (c) to compute the approximate theoretical value of the rate. (Note that you can use MATLAB as your calculator!) Compare this number to your result in part (d)