MAT 125 – Applied Calculus 5.3 – Compound Interest.

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Presentation transcript:

MAT 125 – Applied Calculus 5.3 – Compound Interest

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 Compound Interest 2

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

4 Formulas Dr. Erickson

Formulas Dr. Erickson Compound Interest 5

Example 1 Dr. Erickson Compound Interest 6

Example 2 Dr. Erickson Compound Interest 7

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 Compound Interest 8

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

Continuous Compound Dr. Erickson Compound Interest 10

Example 4 Dr. Erickson Compound Interest 11

Example 5 Dr. Erickson Compound Interest 12

Example 5 Dr. Erickson Compound Interest 13

Example 6 Dr. Erickson Compound Interest 14

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 Compound Interest 15