The document describes the evolution of future value (FV) and present value (PV) models in system dynamics. It outlines several models that were developed to address limitations, such as only supporting simple interest rates, fixed time steps, or isolated goals. The most advanced model supports FV or PV goal seeking, dynamic policies for interest/discount rates, continuous or discrete events, and produces results for any time period or until goals are reached. A unified causal loop diagram and model were also developed to integrate the FV and PV perspectives.

1. The Evolution of FV & PV Models “System Dynamics Applied to the Value of Money” Author: Victor German Ledesma Garcia Assessor: Roberto Osorno Hinojosa October 2006

2. Popular prototype for Future Value Characteristics: It only contains simple interest rate. Limit: It doesn’t support sub periods for capitalization. Problem: The result for Final Amount changes when time step changes.

3. Model with Effective Interest Rate Characteristics: It contains effective interest rate. Limit: Results for sub periods of time step can’t be obtained. Problem: The result for Final Amount changes when time step changes.

4. Model with Effective Interest Rate in Time Characteristics: It contains effective interest rate in time, supports sub periods for capitalization. Limit: It’s isolated to goals focus. Vantage: The result for Final Amount can be obtained for any sub period of capitalization and settings in time step.

5. Causal Loop Diagram for Future Value Model Toward to Goals Discrepancy controls the addition of Revenues. There is a reinforcing loop in Discrepancy – Liquid Value – Revenue.

6. Model with Effective Interest Rate in Time applying Goals Characteristics: It contains effective interest rate in time plus goal focus. Limit: It doesn’t support floating interest rate. Vantage: It produce results for any time and It can be stopped when goal is reached.

7. Causal Loop Diagram for FV oriented to Goals and Floating Interest Rate It just needs a link between Liquid Value and “i” for policies of changes.

8. Model with Effective Interest Rate in Time applying Goals and Policies Characteristics: Complete to support goals and policies of changes in Interest Rate. Limit: The results can’t be reverted in time. Vantage: It produce results for any time and It can be stopped when goal is reached.

9. Causal Loop Diagram for Present Value Model Toward to Goals The main difference now are discounts over time.

10. Model with Effective Discount Rate in Time applying Goals and Policies Characteristics: Complete to support goals and policies of changes in Discount Rate. Limit: The results can’t be reverted in time. It is isolated from FV model. Vantage: It produce results for any time and It can be stopped when goal is reached.

11. Unified Causal Loop Diagram for Future and Present Value

12. Unified Diagram for FV & PV Characteristics: Unified able to support FV or PV goal seeking and policies. Continuous or Discrete events can be selected.