© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

The Rule of 72

The most important and simple rule to financial

success.

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Simply put

72Is a

Magical Number

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

What is the rule of 72?It can tell you:

1) How many years it will take an investment to double at a given interest rate using compounding interest.

2) How long it will take debt to double if no payments are made.

3) The interest rate an investment must earn to double within a specific time period.

4) How many times money (or debt) will double in a specific time period.

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

1) How long will it take for our investment to double

When 72 is divided by the interest rate, the answer is the number of years it will take the investment to double.

EXAMPLE: We know our interest rate is 10% on our

investment.

TO FIGURE THIS:72 ÷ 10 = 7.2 YEARS TO DOUBLE

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

ANOTHER EXAMPLE: Compound Interest is 8% How long will it take for the investment to double?

72 divided by 8% = 9 years

At the end of nine years, the initial savings of $100 will have increased to $200 — which is double the amount of initial savings

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

How long it will take debt to double if no payments are made

You borrow $1,000 from a friend, who is charging 6% interest. If you do NOT make ANY payments, how long will it take for your debt to double?

72 ÷ 6 = 12 YEARS FOR DEBT TO DOUBLE

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

The interest rate an investment must earn to double within a specific time period

If a person would like his/her investment to double in 4 years, you would calculate it like this –72 ÷ 4 = 18% interest rate is required on the investment

ANOTHER EXAMPLE: Would like investment to double in 6 years

Need 12% interest rate for investment to double in 6 years

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

How many times money (or debt) will double in a specific time period

For example, if a person earns 6% on a $50,000 investment it will take 12 years to double (72/6=12).

YEARS INVESTMENT1 $50,000

12 $100,000

24 $200,000

36 $400,000

48 $800,000

60 $1,600,000

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

You must remember a few things about the “Rule of 72”

The “Rule of 72” Is only an approximation The interest rate must remain constant The equation does not allow for

additional payments to be made to the original amount

Interest earned is reinvested Tax deductions are not included within

the equation

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

???????????????????????????

Where did the Rule of 72 come

from?

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© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Albert Einstein

“It is the greatest mathematical

discovery of all time.”

Credited for discovering the mathematical equation for

compounding interest, thus the

“Rule of 72”

T=P(I+I/N)YN

*(Notes below)

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Albert Einstein

Einstein discovered this simple

equation for compounding

interest that allows people to easily understand the time value of

money.

Time Value of Money is a calculation that adjusts for the fact that dollars to be received or paid out in the future are not equivalent to those received or paid out today because of

compounding interest.

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

REVIEW OFRULE OF 72

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© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

WHAT IS COMPOUNDING INTEREST

Compounding interest is

Interest earning interest on interest!

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Nathan’s Certificate of Deposit

Invested $2,500 Interest Rate is 6.5%

72 = 11 years to double investment

6.5%

Nathan invested $2,500 into a Certificate of Deposit earning a 6.5% interest rate. How

long will it take Nathan’s investment to double?

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Another ExampleThe average stock market return

since 1926 has been 11%

72 = 6.5 years to double investment

11%Therefore, every 6.5 years an individual’s investment in the

stock market has doubled

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Jessica’s Credit Card Debt

$2,200 balance on credit card 18% interest rate

72 = 4 years to double debt

18%

Jessica has a $2,200 balance on her credit card with an 18% interest rate. If Jessica chooses to not make any payments and does not receive late charges, how long

will it take for her balance to double?

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Another Example:

$6,000 balance on credit card 22% interest rate

72 = 3.3 years to double debt

22%

How long will it take for debt to double?

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Jacob’s Car

$5,000 to invest Wants investment to double in 4 years

72 = 18% interest rate

4 years

Jacob currently has $5,000 to invest in a car after graduation in 4 years. What interest

rate is required for him to double his investment?

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Another Example

$3,000 to invest Wants investment to double in 10 years

72 = 7.2% interest rate

10 years

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Rhonda’s Treasury Note

72 = 9.6 years

7.5% to double investment

Age Investment

22 $2,500

31.6 $5,000

41.2 $10,000

50.8 $20,000

60.4 $40,000

70 $80,000

Rhonda is 22 years old and would like to invest $2,500 into a U.S. Treasury Note earning 7.5%

interest. How many times will Rhonda’s investment double before she withdraws it at age 70?

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Another Example $500 invested at age 18 7% interest How many times will investment double before age 65?

72 =10.3 years

7% to double investment

Age Investment

18 $500

28.3 $1,000

38.6 $2,000

48.9 $4,000

59.2 $8,000

69.5 $16,000

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

THE END

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© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

TaxesA person can choose to invest into two

types of accounts:Taxable Account – taxes charged to

earned interestTax Deferred Account – taxes are

not paid until the individual withdraws the money from the investment

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Taxes ExampleGeorge is in the 33% tax bracket. He

would like to invest $100,000. George is comparing two accounts that have a 6% interest rate. The first is a taxable account charging

interest earned. The second account is tax deferred until he withdraws the

money. Which account should George invest his money into?

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© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Effects of taxes

Years Taxable

Tax Deferre

d

12 $200,000

18 $200,000

24 $400,000

36 $400,000

$800,000

Taxable Account Earning 4% after taxes

72 =18 years

4% to double investment

Tax Deferred Account

72 = 12 years

6% to double investment

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Conclusion The Rule of 72 can tell a person:

How many years it will take an investment to double at a given interest rate using compounding interest;

How long it will take debt to double if no payments are made;

The interest rate an investment must earn to double within a specific time period;

How many times money (or debt) will double in a specific time period.

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

Conclusion continued Things individuals must remember about

the Rule of 72 include: Is only an approximation The interest rate must remain constant The equation does not allow for additional

payments to be made to the original amount Interest earned is reinvested Tax deductions are not included within the

equation

1.14.3.G1

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Rule of 72Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences

at the University of Arizona

ASSIGNMENT

- Rule of 72 Worksheet (1.14.3.A1)

- Rule of 72 Math (front & back)

- Compounding Interest Quarterly