The following information is available for a bank account:

Note that the money earns interest which is computed as
Interest = iBi
where i = the interest rate expressed as a fraction per month, and Bi 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

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 = iB.
(c) Use Euler's method with a time step of 0.5 month to simulate the balance. Assume that the deposits and withdrawals are applied uniformly over the month.
(d) Develop a plot of balance versus time for (a) and (c).

Date Deposits Withdrawals Interest Balance 1522.33 20.13 327.26 216.80 378.5 106.80 27.31 350.61 dB = f(D(t), w(t), i) dt