1.3 The following information is available for a bank account: Date Deposits Withdrawals Balance 5/1 1512.33 220.13 327.26 6/1 216.80 378.61 7/1 450.25 106.80 8/1 127.31 350.61 9/1 Note that the money earns interest which is computed as iBi Interest fraction per month, where i the interest rate expressed as a and B, the initial balance at the beginning of the month. (a) Use the conservation of cash to compute the balance on 6/1, 7/1, 8/1, and 9/1 if the interest rate is 1% per month (i 0.01/month). Show each step in the computation. (b) Write a differential equation for the cash balance in the form dB =f[D( ), W(t), i] dt where t time (months), D(t) = deposits as a function of time ($/month), W(t) = withdrawals as a function of time ($/month). For this case, assume that interest is compounded continuously; that is, interest (c) Use Euler's method with a time step of 0.5 month to simulate the balance. Assume that the deposits and with- drawals are applied uniformly over the month. a plot of balance versus time fol (a) and (c). iB. (d) Develop