Cool math fractal

math image

math image

cool math pre-algebra lessons: how to...cool math algebra lessons: how to...cool math precalculus / calculus lessons: how to...cool math anxiety survival and success guidecool geometry art - fractals, polyhedra, morebrain benders and free online jigsaw puzzlesCool Math Algebra, Precalulus and math anxiety booksother math stuff
cool math lessonscool math games and practice problemscool math gamesfree online math dictionarygeometry trigonometry reference area
cool math for teacherscool math for parentsCool Math 4 KidsCoolified GamesFinance FREAKTotally Stressed OutScience Monster

Coolmath Algebra
Exponentials & Logarithms Lesson 4 - Continuous Compound Interest  (page 1 of 2)
---- This algebra lesson explains how continuous compound interest works and where the formula comes from

math image

Now available:  Coolmath Algebra books!  Part 1, Part 2 and Part 3 covering the Algebra you need from Algebra 1 through Precalculus Algebra (Beginning Algebra through College Algebra)

other Coolmath Books:  Coolmath Precalculus Review (the math you really need to survive Calculus 1) and Math Survival Guide (How to conquer math and deal with math anxiety)

line
Graphing Calculator Scientific Calculator << a new window will open for these
line
So, we learned that the more times we compound, the more money we make...  What if we could compound continuously?

Let's figure out how the formula for this would work:

We'll invest $1.00 at 100% interest for one year and we'll keep increasing the compounding and see what happens.

       A quick example, so you can follow this:

$1.00 compounded quarterly at
100%
interest for 1 year...

initial amount = $1

split factor = 1.25

number of splits = 4

final amount = 1 * ( 1.25 )^( 4 ) = approximately $2.4414... ... we can leave off the 1

 


TRY IT:

Do the same for compounded monthly.


Let's make a table:

TIMES COMPOUNDED     AMOUNT
annually     $2
semi-annually     $2.25
quarterly   $2.4414062...
monthly   $2.6130352...
100 times   $2.7048138...
1000 times   $2.7169239...
10,000   $2.7181459...
100,000   $2.718268...
1,000,000   $2.7182804...

Look at what's happening here.  arrow

Not changing very much anymore, are they?

In fact, they are getting closer and closer to a very special number

e = approximately 2.7182818

It's an irrational number like pi.  It goes on forever and ever and never repeats.

We won't be able to use the split factor for continuous compounding, BUT we WILL be able to use this e guy...  and he came from the split factor!

Continued on the next page

 The printing and distribution and/or downloading of these lessons is strictly prohibited.

line
Graphing Calculator Scientific Calculator << a new window will open for these
line

.....:::::::::::::::  HELP SUPPORT COOLMATH  :::::::::::::::.....
:::::::  link to us   :::::::   advertise with us  :::::::  why we have ads  :::::::  cool math games store  :::::::

 ||   about us   ||  about our Cool Math Games  ||   safe surfing   ||   privacy policy   ||   terms of use   ||   copyrights & fair use   ||
 
||  cool math pre-algebra  ||  cool math algebra  ||  cool math precalculus / calculus  ||  cool math anxiety survival  ||  geometry / art / fractals / polyhedra  ||
||  free online brain bender and jigsaw puzzles  ||  cool math books  ||  other math stuff  ||
||  cool math lessons: how to...  ||  cool math games & practice problems  ||  cool math 4 kids lessons and games  ||  cool math games for arithmetic  ||
||  free online math dictionary  ||  geometry / trigonometry reference  ||  cool math for teachers  ||  cool math for parents  ||  cool math games  ||
 
||  Coolified Games  ||  Cool Math 4 kids  ||  Spike's Game Zone  ||  Finance Freak  ||  Totally Stressed Out  ||  Science Monster lessons  ||

Thanks for visiting Coolmath.com
© 1997-2012 Coolmath.com, Inc.