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As you think about the Savings Account model, isn't there something missing? If you can put money in a Savings Account and it grows over time then why isn't everybody rich? There must be something missing. In this section we'll investigate some additional aspect of the Savings Account model.

Contents 1 Growth Potential 2 Interest Period 3 Additional Enhancements 3.1 Period & Interest 3.2 Deposits 3.3 Withdrawals 4 Observations and Insights 5 References

[edit] Growth Potential

Open the Savings Account model from the previous segment and make the following change:

• Select Simulation Specs... from the Simulation menu and set:
  • stoptime = 40, implying the model will run for 40 years
  • Integration Method = Euler's Method (We'll talk about why later)
• Open the Equation Editor for principal and set the initial value = 1000.
• Open the Equation Editor for interest rate and set the value to 0.1 meaning 10%

Now Run the simulation and you should see the graph in Fig. 2.

Fig. 2 is meant to give you a sense of the implications positive feedback has on growth, and just what an exponential growth curve looks like. What makes exponential growth structures so annoying is that for a long period of time they grow relatively slowly. So slowly that we generally don't really pay attention, or notice the growth, then all of a sudden the change gets large enough to attract our attention and we ask how things got to this state. Consider paddling down the river in a canoe. There is generally calm waters just before the falls, and once you realize you're at the falls it's too late.

Software Note: If you open the Graph Editor and click on the Data Grid icon, 4th from the right, a table of values for each point on the graph will be displayed in a scrollable table with the value of principal at the end of each year. At the end of year 40, with a $1,000 initial principal, the principal is $45,259.26 Rather sizeable, though it took 40 years.

At this point you might take a moment to think about where you have experienced reinforcing structures either in your personal life or in the news. They are very common.

[edit] Interest Period

There are savings institutions that pay interest other than annually, which is how this model is currently set up. Imagine for a moment that you set up a savings account in a bank that pays interest quarterly rather than annually. This is called quarterly compounding.

Select Simulation Specs... set dt = .25. This indicates that the model is supposed to step through from starttime to stoptime .25, or quarterly, increments. Run the model and you should now have a display that looks like Fig. 2.

Notice that the second Principal trend is larger than in Fig. 2. If you look at the Data Grid the final value of principal after 40 years is $51,977.87, which is about $6,718 dollars more than in the previous example. This should provide you with a sense of the value of compounding interest in shorter and shorter time frames.

Model Note: When you develop a model the period for dt should be set to the period that you want to check what's happening with the model. The dt should be set at a value small enough to ensure relevant interactions are not missed during the simulation run. A quick way to check if dt is small enough is to run the model, cut dt in half and see if the results are different. If so then use the smaller dt, and repeat the check. You can check by increasing dt also. Generally the smaller dt the more accurate the model, though the longer it will take for it to run.

Also this example was a bit contrived because the Euler Method was selected, which is less accurate, just so the output would be chunky and the difference would should up with different values of dt. Generally you want to use a value of dt where making it smaller doesn't change the output value.

[edit] Additional Enhancements

Since it's your savings account you can deposit additional funds and make withdrawals as you like, though each has consequences. You are now going to make 4 modifications to the model:

• 60 Year Period: set the model to run for 60 years
• Monthly Interest: implying your savings account is in a place that pays you interest monthly
• Deposits: lets you add additional money to the principal monthly
• Withdrawals: lets you withdrawal from the savings account monthly

[edit] Period & Interest

The easiest way to set this up is to go to Simulation Specs and set:

• starttime = 0
• stoptime = 720 (60 years in months)
• dt = 1 (monthly)
• Integration Method = Euler's Method

[edit] Deposits

Now modify your model to look like Fig. 4.

Model Note: MapSys automatically updated the equation for principal, behind the scenes, when you added the deposits flow.

Here are the equations to enter in the Equations Editor.

• months per year = 12
• interest rate = .05
• monthly interest rate = interest rate / months per year
• interest = principal * monthly interest rate
• deposits = 100

Model Note: MapSys ads an underscore "_" in variable names for space and enter so it can keep track.

We've now have a Savings Account with an initial deposit of $1,000 and monthly deposits of $100. The model runs for a period of 60 years, in monthly increments, with a 5% annual interest rate compounded monthly.

If you wanted to create a retirement Savings Account over a period of 40 years you can be rather certain the interest rate won't be the same over all those years, though it might average out to be around 5%. With this scenario at the end of 40 years you would have $159,960.43 dollars in your retirement account. So now lets look at withdrawals.

[edit] Withdrawals

Let's now make some changes to the model which allow us, after some period of time to start withdrawing money from what is now a Retirement Account. Add a withdrawal flow with amount and starting when as Auxiliary inputs to withdrawals as in Fig. 5.

Now make the following updates with the Equations Editor:

• amount = 1000 (withdraw $1,000 a month)
• starting when = 480 (after 40 years)
• withdrawals = if (time > starting_when, amount, 0)
• principal was automatically updated so withdrawals subtracts from principal

Now run the simulation and you should now have a display that looks like Fig. 6, which indicates that after 40 years you can begin withdrawing $1,000 a month for 20 years and not run out of funds, and you're not really getting close. You will have at the end of 60 years $66,686.2.

You can adjust variables and run the simulation to see the impact on principal. While there are numerous other dimensions you might add to this model I think we'll stop here.

[edit] Observations and Insights

As to why this doesn't develop for most, the larger the principal becomes the more attractive it becomes and we think of lots of things we can do with it, so we buy now, don't wait till retirement and the retirement account doesn't develop.

In the next module we'll look at project completion to identify another basic structure.

Prev: Savings Account * Next: Project Completion

[edit] References

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