Chapter 1, Problem 6P

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 $=i{B}_i$

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 theinterest rate is 1% per month $\left(i=0.01/\text{month}\right)$. Show each step in the computation.

(b) Write a differential equation for the cash balance in the form

$\frac{dB}{dt}=f\left(D\left(t\right),W\left(t\right),i\right)$

where $t=$ time (months), $D\left(t\right)=$ deposits as a function of time ($/month), $W\left(t\right)=$ 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).