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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

7.2 Compound Interest and Exponential Growth

©2001 by R. Villar

All Rights Reserved

compound interest and exponential growth

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:

slide3

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...

exponential growth

Exponential Growth:

16

12

8

4

Balance (1000 dollars)

0 2 4 6 8 10

Time (Years)

exponential growth5

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