The following information is available for a bank account:

The money earns interest which is computed as Interest = i B_i where i = the interest rate expressed as a fraction per month, and B_i 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).

Transcribed Image Text:

Date Deposits 5/1 6/1 7/1 8/1 9/1 220.13 216.80 450.25 127.31 Withdrawals 327.26 378.61 106.80 350.61 Balance 1512.33