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

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.

Not changing very much anymore, are they?

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

It's an irrational number like .  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