**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**