Compound Interest & Rule of 72
Albert Einstien called it the most powerful
thing he had ever witnessed.
Compound interest is a fact of life. The only
real choice you have is whether you will have compound interest
working for you in savings or against you in debt. But what
exactly is compound interest? And what is the "Rule of 72"?
[SPECIAL NOTE: Many thanks to the links at the upper right Elsewhere
on the Web. Though the material is universally available
and therefore public knowlege, recognition should still be
issued for my "re-education"]
Compound Interest Defined
- Let's start by illustrating what compound interest is all
about. We all know interest is computed on an account balance
(i.e. a savings account). But when interest is added to the
account versus returning it immediately to the customer, the
interest itself earns interest during the next time period for
The time interval between the occasions at
which interest is added to the account is called the
Compounding Period. The interest rate (normally stated as
an annual % in decimal format and sometimes called the nominal
rate), together with the compounding period and the balance in
the account, determines how much interest is added in each
compounding period. The basic formula is this:
Interest rate (r) X Principle
(P) or balance = the interest to be added (I)For
example: If an Interest rate of 6% (r) were applied to a
Principle (P) of $10,000, the interest (I) would be $600.
$10000 X 6% = $600
The compound Interest Equation is:
P = A (1 + r/n)^nt
- P = the principal (current worth)
- A = the initial amount on deposit
- r = the interest rate (expressed as a
fraction: ex: 6% = .06)
- n = the number of times per year that
interest is compounded
- t = the number of years invested
NOTE: The above might be more easily understod
thinking in terms of a Simplified Compound Interest .
When interest is only compounded once per yer (n=1), the
equation simplifies to: P = A (1 + r)^t
- P = $10,000 X (1 + .06) X 1 year
- P = $10,600
The following table shows the final principal
(P), after t = 1 year, of an account initally with P = $10000,
at 6% interest rate, with the given compounding (n).
- n P
- 1 (yearly) $ 10600.00
- 2 (semi-anually) $ 10609.00
- 4 (quarterly) $ 10613.64
- 12 (monthly) $ 10616.78
- 52 (weekly) $ 10618.00
- 365 (daily) $ 10618.31
- continuously $ 10618.37
As you can see, there is an advantage to
compounding more frequently. If the balance, interest rate and
length of the deposit all remain the same, more interest can be
earned by increasing the compounding periods per year. With the
information above and armed with the "Rule of 72" information
below, you can start to understand why a $100,000 home over a 30
year loan period can actually cost over $300,000.
[Special note: When interest
is compounded continually (in other words, when 'n' approaches
infinity), the compound interest equation takes the form:
P = A e rt where e is approximately 2.71828
(the exponential number).
The "Rule of 72" -
allows you to determine the number of years
before your money doubles... whether in debt or investment. Here
is how to do it:
Divide the number 72 by the percentage rate
you are paying on your debt (or earning on your investment).
For example: You borrowed $1,000 at 6%
interest. 72 divided by 6 is 12. That makes 12 the number of
years it would take for your debt to double to $2,000 if you did
not make any payments. Similarly, A savings account with $500
deposited in it earning 4% interest. 72 divided by 4 is 18. It
will take 18 years for your $500 to double to $1,000 if you
don't make any deposits.
Now, consider compounding the compound
interest or doubling the Rule of 72. See what happens each time
your money doubles...
$1 ... $2 ... $4 ... $8 ... $16 ... $32 ...
$64 ... $128 ...Consider how fast your debts can double with
high interest rates, such as those charged on most credit card
accounts. On the ther hand, think what happens cashing in a long
term mutual fund. Compound interest is like a mushroom cloud...
the longer it exists, the more powerful a force it becomes...
working for you or against you.
Adding Fuel To The Fire -
Now permit me to put it all into
perspective while adding fuel to the fire. In the article
Balance Transfer and Consolidation you will find a couple very
interesting tables. One of these tables offers information on
applying the minimum monthly payment on a credit card which is
typically 2%-3% of the outstanding balance. See what happens
when varying the minimum payments. The table is based upon a
$5000 balance and a 17% interest rate.
You will soon discover that though the minimum
monthly payment is dramatically reduced with a lower % minimum
payment, the tota interest paid and years to pay off become
astronomical. By reducing the minimum paymetn by 1/2, the years
to payoff increases from 18 years to 80 years. The interst paid
raises from $4200 to over $25000.
Now ask yourself "Is compound interest working
for or against you?"