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7.2 Compound Interest and Exponential Growth

7.2 Compound Interest and Exponential Growth . ©2001 by R. Villar All Rights Reserved. Compound Interest and Exponential Growth. A is the balance in the account after t years P is the principal (amount deposited) N is the number of compounding periods per year r is the interest rate.

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7.2 Compound Interest and Exponential Growth

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  1. 7.2 Compound Interest and Exponential Growth ©2001 by R. Villar All Rights Reserved

  2. Compound Interest and Exponential Growth Ais the balance in the account after t years Pis the principal (amount deposited) Nis the number of compounding periods per year ris the interest rate Simple Interest: the amount paid or earned for the use of money for a unit of time. Compound Interest: Interest paid on the original principal and on interest that becomes part of the account. Compound Interest Formula:

  3. Example: You deposit $10,000 in an account that pays 5% annual interest compounded quarterly. What is the balance after 10 years? A ≈ $16,440 This is an example of exponential growth. Let’s look at the graph of this problem which will demonstrate exponential growth...

  4. Exponential Growth: 16 12 8 4 Balance (1000 dollars) 0 2 4 6 8 10 Time (Years)

  5. Exponential Growth: Notice that this quantity is greater than 1. If it was less than 1, the graph would reflect Exponential Decay. Exponential Growth and Decay Model y = Cax Let a and C be real numbers, with C > 0 , If a < 1, the model is exponential decay If a > 1, the model is exponential growth

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