Question

The following information is available for a bank account:
Date Deposits Withdrawals Interest Balance
5/1 1522.33
220.13 327.26
6/1
216.80 378.51
7/1
450.35 106.80
8/1
127.31 350.61
9/1
Note that the money earns interest which is computed as
Interest 5 i Bi
where i 5 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 5
0.01/month). Show each step in the computation.
(b) Write a differential equation for the cash balance in the form
dB
dt
5 f (D(t), W(t), i)
where t 5 time (months), D(t) 5 deposits as a function of time
($/month), W(t) 5 withdrawals as a function of time ($/month).
For this case, assume that interest is compounded continuously;
that is, interest 5 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).

Answer 1