Final Write Up:

Dicrete Dynamical Systems Using Excel

Zachary Laughlin


The Problem:

After Jack graduated from highschool, he started working at his dads mechanics shop. Every month Jack makes 500 dollars and put his earnings into a savings account that build interest with a rate of .2% After 3 years working under his dad, Jack decides he want to pursue a college education. Jack also recieves a full ride scholorship to pay for college. Jack wants to know how much money he has saved over the last 3 years, and how much money a month he can spend through the three years of community college where his saving account will be at zero?

The Solution:

By using a spread sheet, we can figure out how much money Jack has saved. We can also figure out how much money he can spend a month through college so his savings account balence in zero. Below is the spreadsheet on Jacks monthly earning with an interest rate of .2% each month.

So after 3 years of working under his dad, Jack has saved up $18,644.52. I used some excel formula to make calclations easy. I started by putting in an index of months. I then plug in $500 for the first month. In the next cell down, I plugged in the equation =500*(1.002)+500. The 1.002 represents the previous months balence with interest and the +500 represents the $500 dollars that he makes each month.

Now let's see how much Jack can spend each month in college to get his accont to zero. Excel spreadsheet below:

By using a guess and check method, I took Jacks total balance of 18644.52 put it in the cell representing his first month in college. I still had to take into account that the savings would still be drawing interest even after he takes out the "x" amount of money each month. So I used the equation: 18644.52*(1.002)-552.07. Again, the 1.002 represents the balence each money drawing interest upon itself. The 552.07 is the amount that Jack can withdraw each month in order to get his saving account to a balance of zero. As the excel spreadsheet shows, his account does not get exactly to zero, but after three years of spending, he will only have a mere 9 cents in his savings account.