Mathematical modeling (difference equations)

18. You are counseling a recent graduate on retirement planning. You es- timate he will earn 9% per year (or 0.75% per month) on a retirement account. With his high-paying job, he will be able to invest Rupees 5000 per month initially. To allow for inflation and pay raises, you suggest increasing this amount by 0.5% per month. Assume that he makes his first deposit at the end of his first month of employment. (i) Formulate a discrete dynamical system that models the amount in this person's retirement account and solve it. (ii) Graphically, determine the balance in the account after 20 years and use the analytic solution to verify it. (iii) How does the analytic solution change if the monthly investment increases by 0.75% per month instead of 0.5% per month? 18. You are counseling a recent graduate on retirement planning. You es- timate he will earn 9% per year (or 0.75% per month) on a retirement account. With his high-paying job, he will be able to invest Rupees 5000 per month initially. To allow for inflation and pay raises, you suggest increasing this amount by 0.5% per month. Assume that he makes his first deposit at the end of his first month of employment. (i) Formulate a discrete dynamical system that models the amount in this person's retirement account and solve it. (ii) Graphically, determine the balance in the account after 20 years and use the analytic solution to verify it. (iii) How does the analytic solution change if the monthly investment increases by 0.75% per month instead of 0.5% per month