1. MAT 125 – Applied Calculus 5.3 – Compound Interest

2. Today’s Class  We will be learning the following concepts today:  Exponential Functions & Their Graphs  Logarithmic Functions & Their Graphs  Properties Relating Exponential and Logarithmic Functions  Compound Interest  Effective Rate of Interest  Continuous Compounding of Interest Dr. Erickson 5.3 - Compound Interest 2

3. Introduction  Compound interest is a natural application of the exponential function to the business world. Dr. Erickson 5.3 - Compound Interest 3

4. 4 Formulas Dr. Erickson

5. Formulas Dr. Erickson 5.3 - Compound Interest 5

6. Example 1 Dr. Erickson 5.3 - Compound Interest 6

7. Example 2 Dr. Erickson 5.3 - Compound Interest 7

8. Effective Rate of Interest  The effective rate is the simple interest rate that would produce the same accumulated amount in 1 year as the nominal rate compounded m times per year. Dr. Erickson 5.3 - Compound Interest 8

9. Example 3  Find the effective rate corresponding to the given nominal rate. Dr. Erickson 5.3 - Compound Interest 9

10. Continuous Compound Dr. Erickson 5.3 - Compound Interest 10

11. Example 4 Dr. Erickson 5.3 - Compound Interest 11

12. Example 5 Dr. Erickson 5.3 - Compound Interest 12

13. Example 5 Dr. Erickson 5.3 - Compound Interest 13

14. Example 6 Dr. Erickson 5.3 - Compound Interest 14

15. Next Class  We will discuss the following concepts:  The Derivative of the Exponential Function  Applying the Chain Rule to Exponential Functions  Please read through Section 5.4 – Differentiation of Exponential Functions in your text book before next class. Dr. Erickson 5.3 - Compound Interest 15