Brief Description: This three-part activity asks students to: (1) derive a general interest rate formula, and (2) simulate and examine the growth of money at several different interest rates and compounding periods. Extension activities look at extreme compounding periods.

Mathematics Topics: This activity involves applying exponential functions and parametric equations and graphing to problems involving simple and compound interest.

Mathematical Thinking: Students will estimate the growth of money at different interest rates, derive basic compound interest equations, apply and generalize these equations, simulate growth with parametric equations, and assess their methods and the reasonableness of their estimations.

Technology: Students will use graphing calculators to calculate exponential quantities, graph parametric equations, label graphs, and trace graphs.

Sample Screen Shots:
Below are illustrative calculator screen shots.

Figure 1. A simulation of the growth of a $1,000 investment at 5% (money market), 8% (bonds) and 16% (stocks) monthly for 20 years, compounded monthly

Figure 2. A graph of the relationship between accumulation and compounding period for a very special case.