# Deterministic Model Example

*by Jon Wittwer, PhD*

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A **deterministic model** is a model that gives you the same exact results for a particular set of inputs, no matter how many times you re-calculate it.

An example of a deterministic model is a calculation to determine the **return on a 5-year investment** with an annual interest rate of 7%, compounded monthly. The **model** is just the equation below:

The **inputs** are the initial investment (*P* = $1000), annual interest rate (*r* = 7% = 0.07), the compounding period (*m* = 12 months), and the number of years (*Y* = 5).

One of the purposes of a model such as this is to make predictions and try **"What If?" scenarios**. You can change the inputs and recalculate the model and you'll get a new answer. You might even want to plot a graph of the future value (F) vs. years (Y). In some cases, you may have a fixed interest rate, but what do you do if the interest rate is allowed to change? For this simple equation, you might only care to know a **worst/best case scenario**, where you calculate the future value based upon the **lowest and highest interest rates** that you might expect.