The following information is available for a bank account:Note that the money earns intere...

The following information is available for a bank account:

Note that the money earns interest which is computed as

Interest = iB_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.

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(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.

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(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.

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(d) Develop a plot of balance versus time for (a) and (c).