Mary, Mary, quite continuously, how does your money grow? Uses examples to examine the difference between simple interest and compound interest, and to take a look at different rates of compounding. Learners explore what would happen as the number of times of compounding approaches infinity and introduces the concept of Euler's number. The last example looks at the difference made between compounding daily and compounding continuously for a year.

Concepts

euler's number, compound interest, simple interest, interest, exponential models, exponential equations, exponential growth

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Additional Tags

math

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Instructional Ideas

• Have the class graph different compound interest equations, varying only the compounding times to view the difference in growth rates
• Create problems with compounded quarterly, monthly, weekly, daily, and continuously for independed practice

Classroom Considerations

• Lesson assumes the class has worked with simple interest

Pros

• The lesson plan provides the steps needed in order to derive the compound interest formulas
• The resource contains a short history and definition for Euler's number

Cons

• The description does not provide a clear explanation on why the substitution of u is needed in the derivation of the continuous compounded formula

Common Core

HSA-SSE.B.3.c HSF-IF.C.8.b MP4 MP7