EBK NUMERICAL METHODS FOR ENGINEERS
EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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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 ( i = 0.01 / month ) . Show each step in the computation.

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

d B d t = f ( D ( t ) , W ( t ) , i )

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 = i B .

(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).

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EBK NUMERICAL METHODS FOR ENGINEERS

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