Use the same reasoning as for the amortization problem to write the difference equation for an individual's savings plan. Let y(k) be the savings balance on the first day of the kth year and u(k) the amount of deposit made in the kth year. Write a MATLAB program to compute y(k) if the sequence u(k) and the interest rate r are given. Specialize to the case where you deposit an amount that increases by the rate of inflation i. Compute and plot the total value of the savings as a function of k if the deposit in the first year is $1000, the yearly interest rate is 6%, and the yearly rate of inflation is 3%. (Hint: For simplicity,
assume that the deposits are made on December 31 of each year, and that the balance statement is issued on January 1 of each year.)