A savings account earns 5% annual interest, compounded quarterly, meaning that it earns 1.25% interest each quarter of a year. You have dollar50,000 in that account on January 1. At the beginning of every quarter of a year you withdraw dollar1000 from that account, with the first withdrawal occurring on April 1. Your account is therefore earning interest each quarter on what was in the account at the beginning of the quarter but is losing money from the amount you withdraw. Let n represent the number of quarters of a year after January 1. Let a(n) represent the amount of money in this account at the beginning of the nth quarter after January 1, just after making the withdrawal for that quarter. This means that a(0) = 50,000 and a (1) 50,000 + 0.0125 times 50,000-1000 = 49, 625. Draw a flow diagram of the situation. Use the flow diagram to generate a dynamical system that models this account. Use the dynamical system to determine the amount in that account after 1 year