# The following information is available for a bank account: Note that the money earns interest which is computed as Interest

## Question:

Note that the money earns interest which is computed as

Interest = iBi

where i = 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 = 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).

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## Step by Step Answer:

**Related Book For**

## Numerical Methods for Engineers

**ISBN:** 978-9352602131

7th edition

**Authors:** Steven C. Chapra, Raymond P. Canale

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