THE RULE OF 72, COMPOUND INTEREST FOR
FINANCIAL SUCESS
FINANCIAL SUCESS
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In finance, the rule of 72, the rule of 70 and the rule of 69 are
methods for estimating an investment's doubling time. The number
in the title is divided by the interest percentage per period to obtain
the approximate number of periods (usually years) required for
doubling. ---------------KNOWLEDGEFINANCIAL.COM
Using the rule to estimate compounding periods
To estimate the number of periods required to double an original
investment, divide the most convenient "rule-quantity" by the
expected growth rate, expressed as a percentage.
For instance, if you were to invest $100 with compounding interest at
a rate of 9% per annum, the rule of 72 gives 72/9 = 8 years required
for the investment to be worth $200; an exact calculation gives
8.0432 years.
Choice of rule
The value 72 is a convenient choice of numerator, since it has many
small divisors: 1, 2, 3, 4, 6, 8, 9, and 12. It provides a good
approximation for annual compounding, and for compounding at
typical rates (from 6% to 10%). The approximations are less accurate
at higher interest rates.
For continuous compounding, 69 gives accurate results for any rate,
This is because ln(2) is about 69.3%; see derivation below. Since
daily compounding is close enough to continuous compounding, for
most purposes 69, 69.3 or 70 are better than 72 for daily
compounding. For lower annual rates than those above, 69.3 would
also be more accurate than 72. ----knowledgefinancial.com
methods for estimating an investment's doubling time. The number
in the title is divided by the interest percentage per period to obtain
the approximate number of periods (usually years) required for
doubling. ---------------KNOWLEDGEFINANCIAL.COM
Using the rule to estimate compounding periods
To estimate the number of periods required to double an original
investment, divide the most convenient "rule-quantity" by the
expected growth rate, expressed as a percentage.
For instance, if you were to invest $100 with compounding interest at
a rate of 9% per annum, the rule of 72 gives 72/9 = 8 years required
for the investment to be worth $200; an exact calculation gives
8.0432 years.
Choice of rule
The value 72 is a convenient choice of numerator, since it has many
small divisors: 1, 2, 3, 4, 6, 8, 9, and 12. It provides a good
approximation for annual compounding, and for compounding at
typical rates (from 6% to 10%). The approximations are less accurate
at higher interest rates.
For continuous compounding, 69 gives accurate results for any rate,
This is because ln(2) is about 69.3%; see derivation below. Since
daily compounding is close enough to continuous compounding, for
most purposes 69, 69.3 or 70 are better than 72 for daily
compounding. For lower annual rates than those above, 69.3 would
also be more accurate than 72. ----knowledgefinancial.com
| THE RULE OF 72 Investment Rule of 72The compound interest rule of 72 was discovered by Albert Einstein. Referring to compound interest, Albert Einstein is quoted as saying: "It is the greatest mathematical discovery of all time." --knowledgefinancial.com Albert Einstein (1879 - 1955) called the compound interest rule of 72 the 8th Wonder of the World - It can work for you, or against you. When you invest it works for you. When you borrow it works against you! knowledge financial group Compound Interest Rule of 72Step 1 of 2: How long does it take my investment capital to double? This step teaches you how to determine the number of years it will take for your investment or debt to double in value. Divide the number 72 by the percentage rate you are paying on your debt, or earning on your investment. Here are two examples... You borrowed $1,000 from your friend, who is charging you 6% interest. 72 divided by 6 is 12. That makes 12 the number of years it would take for your debt to your friend to double to $2,000 if you did not make any payments. -----knowledgefinancial.com You have a savings account with $500 deposited in it. It earns 4% interest from the bank. 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. Remember: 72 divided by the interest percentage is the number of years it takes to double. That is the end of step one. Step two will blow your socks off! We ask that you tell two friends about this web site due to the value of the information we are giving you. Step 2 of 2: How many times will my investment money double? -----------KNOWLEDGEFINANCIAL.COM This step teaches you how important it is for your money to double as many times as possible, and for your debts to double as few times as possible. knowledge financial group Determine how many years you will keep your investment before cashing it in. Divide that by the number of years it will take to double each time, the number you figured out in step one |
An alternative is the Rule of 69 , which is used for daily or continuous compounding. But part of the attraction of
the Rule of 72 is the large number of small whole divisors of 72: 2, 3, 4, 6, 8, 9, 12, 18, 24 and 36. This makes it easier to use.
Yet another alternative is the Rule of 70 , which calculates the number of years for an inflation rate to cause the value of an
investment to drop in half, by dividing the inflation rate into 70. Thus it will take 70/2 = 35 years for an inflation rate of 2% to
cut the value of an investment in half.
The Rule of 120 works reasonably well for calculating the time to triple an investment. 114 or 115 would be more accurate,
but not nearly as divisible. The Rule of 144 works well for calculating the time to quadruple an investment. It is simply
double the Rule of 72. ----------------KNOWLEDGEFINANCIAL.COM
Another useful heuristic can calculate a slight underestimate of the total interest paid on an amortized loan with a level
payment. Multiply the initial loan balance by the interest rate and the term of the loan, and divide the result by 2. For
example, a $10,000 loan with a 4% interest rate and 10 year term would yield total payments of $10,000 * 4% * 10 / 2 =
$2,000, just slightly under the actual result of $2,149. The actual result will always be higher because this is a linear
approximation of the amortization curve, which is a convex curve.
the Rule of 72 is the large number of small whole divisors of 72: 2, 3, 4, 6, 8, 9, 12, 18, 24 and 36. This makes it easier to use.
Yet another alternative is the Rule of 70 , which calculates the number of years for an inflation rate to cause the value of an
investment to drop in half, by dividing the inflation rate into 70. Thus it will take 70/2 = 35 years for an inflation rate of 2% to
cut the value of an investment in half.
The Rule of 120 works reasonably well for calculating the time to triple an investment. 114 or 115 would be more accurate,
but not nearly as divisible. The Rule of 144 works well for calculating the time to quadruple an investment. It is simply
double the Rule of 72. ----------------KNOWLEDGEFINANCIAL.COM
Another useful heuristic can calculate a slight underestimate of the total interest paid on an amortized loan with a level
payment. Multiply the initial loan balance by the interest rate and the term of the loan, and divide the result by 2. For
example, a $10,000 loan with a 4% interest rate and 10 year term would yield total payments of $10,000 * 4% * 10 / 2 =
$2,000, just slightly under the actual result of $2,149. The actual result will always be higher because this is a linear
approximation of the amortization curve, which is a convex curve.
The Rule Of 72
Compound Interest
Financial Success
The compound interest and financial success Rule Of 72 is the most
important and simple rule of financial success. It takes two minutes
and costs nothing to learn the Rule Of 72. Gain financial success
faster when you command the power of compound interest, instead
of allowing compound interest to enslave you.
The Rule Of 72 should be taught in every school. Every young person
should understand compound interest and the simple secret to
financial success, before they begin earning, investing and spending
Compound Interest
Financial Success
The compound interest and financial success Rule Of 72 is the most
important and simple rule of financial success. It takes two minutes
and costs nothing to learn the Rule Of 72. Gain financial success
faster when you command the power of compound interest, instead
of allowing compound interest to enslave you.
The Rule Of 72 should be taught in every school. Every young person
should understand compound interest and the simple secret to
financial success, before they begin earning, investing and spending
Compound Interest
What Does Compound Interest Mean?
Interest that accrues on the initial principal and the accumulated
interest of a principal deposit, loan or debt.
Compounding of interest allows a principal amount to grow at a
faster rate than simple interest, which is calculated as a
percentage of only the principal amount.
KNOWLEDGE FINANCIAL explains Compound Interest
The more frequently interest is added to the principal, the faster the
principal grows and the higher the compound interest will be.
The frequency at which the interest is compounded is established
at the initial stages of securing the loan. Generally, interest tends to
be calculated on an annual basis, although other terms may be
established at the time of the loan.
KNOWLEDGEFINANCIAL.COM
What Does Compound Interest Mean?
Interest that accrues on the initial principal and the accumulated
interest of a principal deposit, loan or debt.
Compounding of interest allows a principal amount to grow at a
faster rate than simple interest, which is calculated as a
percentage of only the principal amount.
KNOWLEDGE FINANCIAL explains Compound Interest
The more frequently interest is added to the principal, the faster the
principal grows and the higher the compound interest will be.
The frequency at which the interest is compounded is established
at the initial stages of securing the loan. Generally, interest tends to
be calculated on an annual basis, although other terms may be
established at the time of the loan.
KNOWLEDGEFINANCIAL.COM
Understanding The Time Value Of Money
What Is Time Value? ---------------KNOWLEDGEFINANCIAL.COM
If you're like most people, you would choose to receive the $10,000 now. After all, three years is a long time to
wait. Why would any rational person defer payment into the future when he or she could have the same amount
of money now? For most of us, taking the money in the present is just plain instinctive. So at the most basic
level, the time value of money demonstrates that, all things being equal, it is better to have money now rather
than later.
But why is this? A $100 bill has the same value as a $100 bill one year from now, doesn't it? Actually, although
the bill is the same, you can do much more with the money if you have it now because over time you can earn
more interest on your money.
Back to our example: by receiving $10,000 today, you are poised to increase the future value of your money by
investing and gaining interest over a period of time. For Option B, you don't have time on your side, and the
payment received in three years would be your future value.
Time Value of Money (TVM) ---------KNOWLEDGEFINANCIAL.COM
What Does Time Value of Money (TVM) Mean?
The idea that money available at the present time is worth more than the same amount in the future, due to its
potential earning capacity. This core principle of finance holds that, provided money can earn interest, any
amount of money is worth more the sooner it is received. Also referred to as "present discounted
value".KNOWLEDGE FINANCIAL explains Time Value of Money (TVM)
Everyone knows that money deposited in a savings account will earn interest. Because of this universal fact,
we would prefer to receive money today rather than the same amount in the future.
For example, assuming a 5% interest rate, $100 invested today will be worth $105 in one year ($100 multiplied
by 1.05). Conversely, $100 received one year from now is only worth $95.24 today ($100 divided by 1.05),
assuming a 5% interest rate.
What Is Time Value? ---------------KNOWLEDGEFINANCIAL.COM
If you're like most people, you would choose to receive the $10,000 now. After all, three years is a long time to
wait. Why would any rational person defer payment into the future when he or she could have the same amount
of money now? For most of us, taking the money in the present is just plain instinctive. So at the most basic
level, the time value of money demonstrates that, all things being equal, it is better to have money now rather
than later.
But why is this? A $100 bill has the same value as a $100 bill one year from now, doesn't it? Actually, although
the bill is the same, you can do much more with the money if you have it now because over time you can earn
more interest on your money.
Back to our example: by receiving $10,000 today, you are poised to increase the future value of your money by
investing and gaining interest over a period of time. For Option B, you don't have time on your side, and the
payment received in three years would be your future value.
Time Value of Money (TVM) ---------KNOWLEDGEFINANCIAL.COM
What Does Time Value of Money (TVM) Mean?
The idea that money available at the present time is worth more than the same amount in the future, due to its
potential earning capacity. This core principle of finance holds that, provided money can earn interest, any
amount of money is worth more the sooner it is received. Also referred to as "present discounted
value".KNOWLEDGE FINANCIAL explains Time Value of Money (TVM)
Everyone knows that money deposited in a savings account will earn interest. Because of this universal fact,
we would prefer to receive money today rather than the same amount in the future.
For example, assuming a 5% interest rate, $100 invested today will be worth $105 in one year ($100 multiplied
by 1.05). Conversely, $100 received one year from now is only worth $95.24 today ($100 divided by 1.05),
assuming a 5% interest rate.
The Role of Money in Our Life
THE ARCHITECTURE OF PROSPERITY ---------------- KNOWLEDGEFINANCIAL.COM
Invest in Yourself
One of the greatest thinkers of our time was Buckminster Fuller, scientist, writer, philosopher. He suggested that everyone
quit their jobs and just go home. And stay there until they fully understood what is and is not necessary to do, what they are
best suited for, most passionate to do, and fulfilled in.
Only then did he recommend that we return to work, bringing those capacities and energies to the table, and even then
doing only what is truly necessary. If we did this, he felt, we would have a vastly improved society.
THE ARCHITECTURE OF PROSPERITY ---------------- KNOWLEDGEFINANCIAL.COM
Invest in Yourself
One of the greatest thinkers of our time was Buckminster Fuller, scientist, writer, philosopher. He suggested that everyone
quit their jobs and just go home. And stay there until they fully understood what is and is not necessary to do, what they are
best suited for, most passionate to do, and fulfilled in.
Only then did he recommend that we return to work, bringing those capacities and energies to the table, and even then
doing only what is truly necessary. If we did this, he felt, we would have a vastly improved society.
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The compound interest and financial success Rule Of 72 is the most important and simple rule of financial
success.
success.
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Citibank,Citifinancial, Citimortgage,
Citigroup
JPMorgan-Chase Financial Services
How & where to find money to invest in
real estate? & How to make the Bank say,
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Learn here the most effective ways to get
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REAL ESTATE FINANCING:
HOW AND WHERE TO FIND MONEY TO BUY A
PROPERTY
COMMERCIAL MORTGAGE LOANS:
COMMERCIAL MORTGAGES, COMMERCIAL
REAL ESTATE FOR INVESTORS
IMPORTANT INFORMATION ABOUT THE
UNITED STATES FIVE [5] BIGGEST
FINANCIAL INSTITUTIONS...
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Mortgage Loan Programs Information
Center. --- Government's general
Information; Local, State, and Federal.--
Bank of America Financial Services
Wells Fargo Financial Services
PNC-National City Mortgage Financial
Services
Citibank,Citifinancial, Citimortgage,
Citigroup
JPMorgan-Chase Financial Services
How & where to find money to invest in
real estate? & How to make the Bank say,
"Yes You're Approved"
TYPE OF MORTGAGES: --WHAT GUIDELINES
ARE REQUIRED FOR A MORTGAGE LOAN?
Learn here the most effective ways to get
the best loan rates, and the best terms
REAL ESTATE FINANCING:
HOW AND WHERE TO FIND MONEY TO BUY A
PROPERTY
COMMERCIAL MORTGAGE LOANS:
COMMERCIAL MORTGAGES, COMMERCIAL
REAL ESTATE FOR INVESTORS
| LISTING YOUR PROPERTY FOR SALE FAST & FOR THE TOP PRICE! ATTENTION SELLERS: LET US HELP YOU SELLING YOUR PROPERTY. WITH US: IS MORE ADVERTISEMENT, MORE EXPOSURE, MORE SHOWINGS, MORE OFFERS, AND MORE MONEY FOR YOUR PROPERTY! CALL: --- SOUTH FLORIDA |
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& Registering a Business.
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''INVESTMENT: MAKE YOURSELF RICHER BY
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Common Car-Buying Mistakes To Know
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Price But what about the Financing?
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numbers, and symbols, the latin words
mean? LEARN MORE...
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Insurance General knowledge!-- Life
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beneficiary.--'' Find Government help Here--//
WAYS TO SAVE MONEY, TO MAKE MONEY,
AND GET OUT OF DEBT. -Blogknowledge"----
UNCLAIMED MONEY, UNCLAIMED
PROPERTIES, FREE GRANTS MONEY COULD
BE YOURS! LEARN MORE...
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CENTER------- .FINANCIAL EDUCATION
TOOLS AND RESOURCES -BK.-
10 Money Resolutions for 2010-- And
Retirement Benefits: ----------.
NEWS-LETTER.. --
How To Make Your First $1 Million; The
Millionaire's Mindset---
Registration.
State Licenses and Permits, Steps to Create
& Registering a Business.
'Find Jobs-' Florida jobs and companies with
openings-- ''- Look For Jobs, Need a Job --
''Workforce Innovation Find Jobs--
'' How and where to apply for unemployment--
'' Food Stamp Program- Department of
Children and Families-Food Stamp- APPLY --
Or Get More Information--
'' Food Stamp Employment & Training (FSET)
Program
--'' Government Help and Resources.. --
''-Find Schools: College, University, Technical
Schools- Medical and Nursing Resources for
Students & professionals. --
''INVESTMENT: MAKE YOURSELF RICHER BY
INVESTING THE RIGHT WAY IN THE RIGHT
PRODUCTS.
..Adult Contents, For Adults Only. You Think
You Know About Sexual Positions; Think
Again... 365 Positions to Learn From.
.Sexuality--
Love Connection--
Relationship--
Free Dating Sites.---
Personal - Family --
Adult BEST Positions --
.News Letter: Tax Saving Business News,
financial news, the world market.
..Biography & History of the world greatest
personalities & politicians,,
..The world worst natural disasters &
earthquakes in the history of humanity,,
.Inventions. Great Inventions and discoveries
of the century,, What are they?
.. HAITI: Things you don't know & what you
must know. Learn More!,,
.. Banking, Finance, Investment Knowledge.
The more you know the closer you are to
accomplish great success--
'' ..''DEALERSHIP-- 7 Car Dealer Extras You
May Not Need, Or You Don't Need At All... Car
Dealer Secrets Revealed..! -- And Five
Common Car-Buying Mistakes To Know
About.. // .AUTO-LOANS -- Great Car, Great
Price But what about the Financing?
AMERICAN DOLLAR. What are the letters,
numbers, and symbols, the latin words
mean? LEARN MORE...
LIFE INSURANCE INFORMATION: Ways to
Reduce Your Life Insurance Premium.
Insurance General knowledge!-- Life
Insurance Distribution, Benefits and
beneficiary.--'' Find Government help Here--//
WAYS TO SAVE MONEY, TO MAKE MONEY,
AND GET OUT OF DEBT. -Blogknowledge"----
UNCLAIMED MONEY, UNCLAIMED
PROPERTIES, FREE GRANTS MONEY COULD
BE YOURS! LEARN MORE...
''GOVERNMENTS GENERAL INFORMATION
CENTER------- .FINANCIAL EDUCATION
TOOLS AND RESOURCES -BK.-
10 Money Resolutions for 2010-- And
Retirement Benefits: ----------.
NEWS-LETTER.. --
How To Make Your First $1 Million; The
Millionaire's Mindset---
LISTING YOUR PROPERTY FOR SALE FAST &
FOR THE TOP PRICE!
ATTENTION SELLERS:
LET US HELP YOU SELLING YOUR PROPERTY.
WITH US: IS MORE ADVERTISEMENT,
MORE EXPOSURE,
MORE SHOWINGS,
MORE OFFERS, AND MORE MONEY FOR
YOUR PROPERTY!
CALL: 786---- SOUTH FLORIDA
FOR THE TOP PRICE!
ATTENTION SELLERS:
LET US HELP YOU SELLING YOUR PROPERTY.
WITH US: IS MORE ADVERTISEMENT,
MORE EXPOSURE,
MORE SHOWINGS,
MORE OFFERS, AND MORE MONEY FOR
YOUR PROPERTY!
CALL: 786---- SOUTH FLORIDA
REAL ESTATE FOR SALE, SEE THE ACTUAL LISTINGS NOW!
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Fast, Easy and Simple. Click Here to Search!
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Fast, Easy and Simple. Click Here to Search!
REAL ESTATE FOR SALE AT Low Prices, Below Market Value, Low Interest rates.
FIND HOMES FOR SALE!. SINGLE & MULTI-FAMILY HERE!
SEARCH FOR CONDOMINIUM, APARTMENTS
SEARCH FOR COMMERCIAL PROPERTIES RIGHT HERE!
SEARCH FOR WATERFRONT PROPERTIES
Motivated Sellers; Selling at Unbelievable Prices... LOOK FOR, FOR SALE PROPERTIES HERE!
Live Your Dream
Search it, Find it, Learn about it, Negotiate it, Buy it.
Obtain and retain our contact information to further assist you.! Click Here to contact us &
get immediate help! --- We're Licensed Realtor & Licensed Mortgage Broker.
CALL THE AGENT AT:
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Let Us Help You Sell Your Real
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For All Real Estate Services
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WHO ARE THINKING ABOUT
SELLING
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Your money grows through
compounding,. Compounding is
made up of three components:
amount investing, time for
compounding , and rate of
return. If you have not saved for
retirement in the past, boost the
amount you invest, but avoid
shooting for an abnormally high
rate of return.
compounding,. Compounding is
made up of three components:
amount investing, time for
compounding , and rate of
return. If you have not saved for
retirement in the past, boost the
amount you invest, but avoid
shooting for an abnormally high
rate of return.
Compound interest
The addition of interest to the principal sum
of a loan or deposit is called compounding.
Compound interest is interest on interest.
It is the result of reinvesting interest, rather
than paying it out, so that interest in the
next period is then earned on the principal
sum plus previously-accumulated interest.
Compound interest is standard in finance
and economics.
Compound interest may be contrasted with
simple interest, where interest is not added
to the principal, so there is no compounding.
The simple annual interest rate is the
interest amount per period, multiplied by the
number of periods per year.
The addition of interest to the principal sum
of a loan or deposit is called compounding.
Compound interest is interest on interest.
It is the result of reinvesting interest, rather
than paying it out, so that interest in the
next period is then earned on the principal
sum plus previously-accumulated interest.
Compound interest is standard in finance
and economics.
Compound interest may be contrasted with
simple interest, where interest is not added
to the principal, so there is no compounding.
The simple annual interest rate is the
interest amount per period, multiplied by the
number of periods per year.
Compound Interest
What is 'Compound Interest'
Compound interest is interest calculated on the
initial principal and also on the accumulated
interest of previous periods of a deposit or loan.
Compound interest can be thought of as “interest
on interest,” and will make a deposit or loan grow
at a faster rate than simple interest, which is
interest calculated only on the principal amount.
The rate at which compound interest accrues
depends on the frequency of compounding; the
higher the number of compounding periods, the
greater the compound interest.
Compound Interest = Total amount of Principal
and Interest in future (or Future Value) less
Principal amount at present (or Present Value)
What is 'Compound Interest'
Compound interest is interest calculated on the
initial principal and also on the accumulated
interest of previous periods of a deposit or loan.
Compound interest can be thought of as “interest
on interest,” and will make a deposit or loan grow
at a faster rate than simple interest, which is
interest calculated only on the principal amount.
The rate at which compound interest accrues
depends on the frequency of compounding; the
higher the number of compounding periods, the
greater the compound interest.
Compound Interest = Total amount of Principal
and Interest in future (or Future Value) less
Principal amount at present (or Present Value)
Discrete Compounding
Discrete compounding refers to the method by which interest is calculated and
added to the principal at certain set points in time. For example, interest may be
compounded daily, weekly, monthly or even yearly.
Discrete compounding is the opposite of continuous compounding, which uses a
formula to compute interest as if it were being constantly calculated and added to
principal.
BREAKING DOWN 'Discrete Compounding'
The frequency with which interest is compounded has a slight effect on an investor's
effective annual yield. For example, suppose you deposit $100 in an account which
earns 5% interest annually.
If the bank compounds interest annually, you will have $105 at the end of the year. If,
on the other hand, the bank compounds interest daily, you will have $105.13 at the
end of the year.
Discrete compounding refers to the method by which interest is calculated and
added to the principal at certain set points in time. For example, interest may be
compounded daily, weekly, monthly or even yearly.
Discrete compounding is the opposite of continuous compounding, which uses a
formula to compute interest as if it were being constantly calculated and added to
principal.
BREAKING DOWN 'Discrete Compounding'
The frequency with which interest is compounded has a slight effect on an investor's
effective annual yield. For example, suppose you deposit $100 in an account which
earns 5% interest annually.
If the bank compounds interest annually, you will have $105 at the end of the year. If,
on the other hand, the bank compounds interest daily, you will have $105.13 at the
end of the year.
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