More on the number e, natural logarithms, and compound interest.

1. THE Exponential
Function
exponential function - quot;equot;
by flickr user jeff_boy50

2. A = AMOUNT of money at the end of
the term
P = PRINCIPLE amount, the amount
originally invested or borrowed
r = RATE of interest as a decimal
number
n = NUMBER of times the principle is
compounded per year
t = TIME in years
Time Principle Rate Interest Balance

3. Who wants to be a millionaire?
What is compound interest?
How does this formula quot;workquot;?
How much money will you have after 5 years if you invest
$300.00 at 6% interest compounded annually? monthly?

4. The number e ...
e=
...
Source: e to 1 000 000 digits

5. The Exponential Function
The Natural Logarithm

6. Who wants to be a millionaire?
It turns out that when interest is compounded
continuously, we use this formula to calculate the total
value of the amount, A, earned on the principal, P, after
any period of time, t.
How much money will you have after 5 years if you invest
$300.00 at 6% interest compounded continuously?
If you invest $300.00 at 6% interest compounded
continuously how long will it take to double your money?

7. The Rule of 72
Here's a handy way to figure out how long your investment will take to
double in value. It is called the Rule of 72.
(Interest Rate %) x (Years to Double) = 72
To find the number of years given a percentage:
Years = 72
(Interest Rate %)
To find the percentage required to double given the years:
Rate = 72
Years
Numbers 72 by flickr user szczel

8. Solve ...

10. Solve ...