Using MATLAB

Suppose one invests $500 per month for 5 years. If the desired total amount after 5 years were $60,000, then the required annual interest rate Icould be determined by the following equation: 2) 500, 1/12 12 1 +--| -| | = 60.000 a) First, rewrite the equation in the form f()-0, where f() is a polynomial. b) 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, fnewt.m and fpnewt.m, which are a relevant function f(I) and its derivative, respectively. Use initial guess xo- 2, and run the loop until the relative eror estimate,for the latest root estimate, x.., is less than a tolerance (TOL) of 10- Store all iterates in a vector, and display this vector as a column. c) Now, modify new tl.m to a new script, newt2 m, by adding lines to compute the ratios eu/ and e.. (e) for each iteration. Use your final estimate from part (a) Call 16 digits) for the exact root in the errors. Store each of these ratios in 2 vectors and display the ratios for all i as column vectors. Use the same initial guess o 2 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? d) Using only the first 3 significant digits of your final root estimate from part (a), also theoretically determine whether or not this is a simple root. Does this confirm your results fromm part (b)