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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
RECOMMENDED
GRADE LEVELS AVERAGE TIME TO COMPLETE
EACH LESSON PLAN IS DESIGNED AND CONTINUALLY EVALUATED “BY EDUCATORS, FOR EDUCATORS.” THANK YOU TO THE FOLLOWING
EDUCATORS FOR DEVELOPING COMPONENTS OF THIS LESSON PLAN.
All
Anticipatory Set & Facilitation: 20 to 30 minutes
Conclusion/Assessment Options: 15 to 45 minutes
Time does not include optional items.
Kathie Beck, Family and Consumer Sciences Educator, Holland, MI
NATIONAL STANDARDS LESSON PLAN OBJECTIVES
The curriculum is aligned to the following national standards: National Standards for Financial Literacy American Association of Family and Consumer Sciences Council for Economic Education National Business Education National Jump$tart Coalition
Upon completion of this lesson, participants will be able to: Apply the “Rule of 72” to decisions Describe how compounding interest works
MATERIALS
MATERIALS PROVIDED IN THIS LESSON PLAN
MATERIALS SPECIFIC TO THIS LESSON PLAN
BUT AVAILABLE AS A SEPARATE DOWNLOAD
MATERIALS TO ACQUIRE SEPARATELY
DEPENDING ON OPTIONS TAUGHT
“Rule of 72” Math 2.4.5.A1 What Do You Know? Part 1 2.4.5.A2 What Do You Know? Part 2 2.4.5.A3 What Do You Know? Part 3 2.4.5.A4 Rule of 72 Vocabulary List 2.4.5.E1 What’s Your Number? Activity cards
2.4.5.H1 Rule of 72 Note Taking Guide 2.4.5.L1
Rule of 72 Answer Key 2.4.5.C1
Rule of 72 PowerPoint presentation 2.4.5.G1
Internet
RESOURCES EXTERNAL RESOURCES
External resources referenced in this lesson plan: U.S. Department of the Treasury: http://www.treasury.gov/resource‐center/data‐chart‐center/interest‐
rates/Pages/TextView.aspx?data=yield BizBasics The Rule of 72: https://www.youtube.com/watch?v=12FsjiVzTMA
TAKE CHARGE TODAY RESOURCES
Similar lessons at a different level: Penny Power Active Learning Tool 3.0.2
Optional lesson plan resources: The Fundamentals of Investing 2.4.4 Time Value of Money Magic Active Learning Tool 3.0.25
RULE OF 72 Advanced Level
www.takechargetoday.arizona.edu
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
Choose to Save 2.4.1 Savings Tools 2.4.3 Understanding Credit Cards 2.6.3 Technology Integration Options Active Learning Tool 3.0.50
CONTENT
EDUCATOR MATERIALS PARTICIPANT READING Materials to support educators when preparing to
teach this lesson plan are available on the Take Charge Today website.
Utilize the Fundamentals of Investing Information Sheet 2.4.4.F1
LESSON FACILITATION
PREPARE Visual indicators to help prepare the lesson
INSTRUCTInstructions to conduct the lesson facilitation
CUSTOMIZE
Potential modifications to lesson facilitation
VOCABULARY ACTIVITY
This lesson is intended as a reinforcement and enhancement for the Savings and Investing Unit. For a full list of activities reference the Vocabulary Reinforcement Activities Active Learning Tool 3.0.36.
ANTICIPATORY SET
What’s Your Number? Approximate time: 10 minutes Materials to prepare: 1 What’s Your Number? Activity card 2.4.5.H1 per group of 3 or 4
Note: Do not share the name of the lesson with participants before conducting the activity.
1. Divide participants into groups of 3 or 4 2. Distribute a What’s Your Number? 2.4.5.H1 card to each group 3. Instruct participants to solve the math problem and keep the answer quiet
a. The answer to all problems is “72” 4. Play the song “If I had a Million Dollars” by the Barenaked Ladies as participants
are working to increase excitement for the content. 5. When all groups (or most) have solved their problem accurately, call on several
groups to share their answer 6. As participants realize all the problems have the same answer, ask, “Does anyone
know what is magical about the number “72”? 7. Explain that in this lesson, they will be learning how they can use “72” to help
make financial decision.
Instead of groups, the problems could be projected on a screen for independent working.
RECOMMENDED FACILITATION
Facilitation: PowerPoint Presentation Approximate time: 15 minutes Materials to prepare: Rule of 72 PowerPoint Presentation 2.4.5.G1
The Rule of 72 Note Taking Guide 2.4.5.L1 is available if desired.
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
Part 1: Rule of 72 1. Slide 1: The Rule of 72
a. State that knowing this simple rule can help when making financial decisions
2. Slide 2: Albert Einstein a. Ask participants how they think Albert could be related to this financial
concept 3. Slide 3: He is credited with discovering the mathematical equation for
compounding interest. This formula allows you to find the future value of an investment.
4. Slide 4: A simplified “estimate,” the Rule of 72” allows you to use mental math to determine the number of years it will take to double your investment.
a. The “Rule of 72” is i. Discuss the definition of the “Rule of 72”
5. Slide 5: What Can the “Rule of 72” Determine? a. Explain that because the number 72 is easily divisible 2, 3, 4, 6, 8, and 9,
mental math makes 72 divided by a given interest rate easy to estimate. b. Explain to participants that the Rule of 72 can be used to calculate more
than just the number of years needed to double an investment. 6. Slide 6: Things to Know about the “Rule of 72”
a. Discuss the important items to know about the Rule of 72. 7. Slide 7: Financial Risk Pyramid
a. Explain that the type of investment one chooses has an impact on how fast an investment will double
b. Point out that the investment tools on the bottom of the pyramid are very safe, but have a low rate of return, and will take longer to double
8. Slide 8: Doug’s Certificate of Deposit a. Complete the calculation as a class.
9. Slide 9: Another Example Using Stock Market Returns a. Explain that if a person invests in the stock market, the average return
has been 11%; one must take into account that some investments made much more and some much less
10. Slide 10: Financial Risk Pyramid a. Point out that stocks in the middle of the risk pyramid are safer than
speculative investments that could have a very high rate of return, but are riskier than a savings account or CD.
11. Slide 11: A Stock Investment Example a. If the current outlook predicts between 4% and 6% average return over
the next few years (5% is the average of 4% and 6%), an investment made today would double in 14.4 years.
b. Ask participants how old they will be in 14.4 years c. At that age, would they be able to use the money that grew from that
investment? Brainstorm possible uses: pay off school loans, down payment on a house or car, investing in own business, reinvest to grow even more
12. Slide 12: Can the Rule of 72 be applied to debt? 13. Slide 13: Jessica’s Credit Card Debt
With only Albert’s face showing, have participants Google what Albert and the Rule of 72 have in common.
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
a. Instruct participants to calculate how long it will take for Jessica’s debt to double.
b. Discuss the correct answer. c. Point out that this is an example of compounding interest working
negatively 14. Slide 14: Another Example, Sylvia’s Debt
a. Instruct participants to calculate how long it will take for the debt to double.
b. Discuss the correct answer. c. Discuss the impact made by the difference of a few percentage points of
interest d. Ask participants to share ideas of what $2,200 could be used for instead
of paying interest on debt. 15. Slide 15: Jacob’s Car
a. Instruct participants to calculate the interest rate Jacob needs to have in order double his investment in 4 years.
b. Discuss the correct answer. c. Point out that The Rule of 72 is also a valuable tool to help a person know
if their goals are realistic and safe. d. The high interest rate needed to achieve this goal could most likely only
be achieved with a speculative investment, which could result in the loss of the principal.
16. Slide 16: Rhonda’s Treasury Note a. Instruct participants to complete the calculation b. Discuss the correct answer
17. Slide 17: Another Example, Seth’s Investment a. Instruct participants to complete the calculation b. Discuss the correct answer c. Explain that this is where the power of compounding interest can be
realized: investments that are allowed to grow and double over time. Optional: The below includes information about taxes and is an optional extension. 18. Slide 18: Taxes
a. Explain the difference between taxable and tax deferred accounts 19. Slide 19: Taxes Example
a. Based on the information given, ask participants to choose for George. 20. Slide 20: Effects of taxes
a. Discuss the fact that the tax deferred account doubles more quickly than the taxed account
b. Explain that taxes will be paid as the investor withdraws money from the account in retirement
c. When making the decision to choose a taxed account or tax‐deferred account, an investor must take into consideration the fact that the tax rate applied to the tax‐deferred account will be unknown until the money is withdrawn
21. Slide 21‐22: Review guidelines regarding the Rule of 72 22. Slide 23: Any questions?
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
CONCLUSION OPTION
Math Worksheet Approximate time: 15 minutes Materials to prepare: 1 “Rule of 72” Math worksheet 2.4.5.A1 per participant
1. Have participants apply their learned knowledge by completing the conclusion
independently or with a partner.
ASSESSMENT OPTION
What Do You Know? Approximate time: Varies based on product participants create Materials to prepare: What Do You Know? Part 1 2.4.5.A2, Part 2 A3 and Part 3 A4 per participant Part 1. Participants create a realistic example as well as an equation to support how they can utilize the Rule of 72. Part 2. Participants survey four people to determine what they know about the Rule of 72. Part 3. Participants creatively share what they determined from their survey experience.
Utilize technology and have participants record those they survey and then make a video of what they learned.
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
Rule of 72 Vocabulary List
TERM DEFINITION
1 Rule of 72 The time it will take an investment to double in value at a given interest rate.
2 Taxable Account Taxes charged on earned interest
3 Tax Deferred Account Taxes are not paid until the individual withdraws the money from the investment.
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
Rule of 72 Note Taking Guide
Total Points Earned
Name
18 Total Points Possible
Date
Percentage Class
What are three things the
Rule of 72 can determine?
What is the Rule of 72? Write the equation for the Rule of 72:
What are important things to know about the Rule of 72?
1.
2.
3.
4.
5.
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
Doug invested $2,500 in a Certificate of Deposit, earning an interest rate of 6.5%, how long will it take his investment to double? (Round your answer to 2 decimal places)
How long will it take to double your investment in the stock market if the average return is 11%? (Round your answer to 1 decimal place)
Jessica has a balance of $2,200 on her credit card, with an interest rate of 18%. How long will it take for her debt to double?
What is a taxable account?
How is a tax deferred account different than a
taxable account?
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
What’s Your Number?
Two quarters
+
Two dimes
+
Two pennies
=____________________
A $1,000 investment earning 7.2%
interest annually will earn
$_______________ in a year.
A suggested way to save money is
to put spare change in a jar at the
end of each day. If a person
contributed, on the average,
$2.40 per day in the month of
April, at the end of the month,
s/he would have $_________
Three $20.00 bills
One $10.00 bill
Two $1.00 bills =
$______________
A person who goes out to lunch
four days a week and spends, on
the average, $4.50 each day
could save $____________ in a
month by bringing lunch from
home.
A strategy for saving money is to put spare change in a container at the end of each day. If a person contributed, on the average, $1.20 per day for 60 days, s/he would have saved
$__________________
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
“Rule of 72” Math Total Points Earned
Name
20 Total Points Possible
Date
Percentage
Class
Directions: Use the “Rule of 72” to answer the following questions.
1. Bryce invested $30,000 in his employee‐sponsored retirement account when he was 29 years old. He is now 65 years old and ready to retire. If he earned an average of 6% on the account, how many times did it double? What is the value at age 65? (2 points)
2. How long will it take the following investments to double? Round answers to two decimal places. (9 points)
Investment Interest Rate
Years to Double
Money Market Mutual Fund 3.1%
Small Company Stock 12.6%
3 year Certificate of Deposit 2.8%
5 year Certificate of Deposit 5.1%
Large Company Stock 11.3%
Government Bond 5.3%
Treasury Bills 3.8%
Money Market Account 2.6%
Savings Account 2.3%
3. Jenny has a $3,000 balance on her credit card. The card has an annual percentage rate of with an 18%. If she makes no payments on her card and no late fees are charged, how long will it take her debt to double? (1 point)
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
4. What if Jenny’s APR was 22%, she makes no payments on her card, and no late fees are charged? (Round
your answer to 2 decimal places) (1 point)
5. Tanner is a high school freshman and has purchased a $500 Certificate of Deposit for college. What interest rate must Tanner earn for his investment to double in 4 years? Could Tanner realistically expect to earn that interest rate on a CD? (1 point)
6. Kari would like to make a down payment on a house. She currently has $7000. What interest rate must
Kari receive for her investment to double in 7 years? (Round your answer to 2 decimal places) (1 point)
7. Jackie’s parents invested $3000 into a common stock earning 6% when she was born. How many times will Jackie’s investment double before age 36? What will her investment be worth? What would Jackie’s investment be worth if her parent’s had waited to invest until she was age 12? (3 points)
8. Approximately how many times will a $50,000 investment, earning 5.54% interest, double from age 25 to age 64? What will the investment be worth? (2 points)
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
What Do You Know? Part 1 Total Points Earned
Name
28 Total Points Possible
Date
Percentage
Class
Directions: Part 1) Follow the prompts below to develop an example to share with your peers and role models. (2 points) Part 2) Survey your friends and role models to find out “what do you know” using your example. Survey two peers and two adults. (8 points) Optional: Record the responses of those surveyed Part 3) Reflect on your conversations and what others know about compounding interest. (18 points)
Create an example using the "Rule of 72" to calculate the length of time it will take an investment
to double.
Example:
Doug invested $2500 into a CD
earning 4% interest. It took his
investment _____years to double
Example Equation:
72/4%=18 years
Your Example: Your Equation:
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
What Do You Know? Part 2
Name of person surveyed_______________________ Peer or Adult (circle one)
Ask: “Do you know how to calculate the number of years it will take an investment to double?” If the answer is “Yes”, have the respondent write the answer below. If the answer is “No”, teach him/her the Rule of 72 and have the respondent sign his/her name below.
Name of person surveyed_______________________ Peer or Adult (circle one)
Ask: “Do you know how to calculate the number of years it will take an investment to double?” If the answer is “Yes”, have the respondent write the answer below. If the answer is “No”, teach him/her the Rule of 72 and have the respondent sign his/her name below.
Name of person surveyed_______________________ Peer or Adult (circle one)
Ask: “Do you know how to calculate the number of years it will take an investment to double?” If the answer is “Yes”, have the respondent write the answer below. If the answer is “No”, teach him/her the Rule of 72 and have the respondent sign his/her name below.
Name of person surveyed_______________________ Peer or Adult (circle one)
Ask: “Do you know how to calculate the number of years it will take an investment to double?” If the answer is “Yes”, have the respondent write the answer below. If the answer is “No”, teach him/her the Rule of 72 and have the respondent sign his/her name below.
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© Take Charge Today – June 2016 – Rule of 72 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences Take Charge America Institute at The University of Arizona
What Do You Know? Part 3
Total Points Earned
Name
18 Total Points Possible
Date
Percentage
Class
Directions: Create a product to share what you learned and experienced during the survey about the Rule of
72.
Products could include utilizing a Web 2.0 such as Glogster, Voki, Animoto
Creation of a video using an app such as Animoto
Writing an essay or letter to your teacher
Creating a cartoon or jingle
Exemplary Satisfactory Unsatisfactory No Performance
Score
Content – Rule of 72: Product clearly shows that the
participant either taught others or learned a new thing from the experience
Product indicates how many were in the “know”
6‐5 4‐3 2‐1 0
Content – Feelings about others being in the “know”: The creator shares his/her opinion
about compound interest being an important concept that should be “known” by others
The creator expresses his/her reasoning of how/why compound interest affects well being
6‐5 4‐3 2‐1 0
Quality of Presentation Materials: Easy to understand Accurate (no errors in content or
grammar) Visually appealing
6‐5 4‐3 2‐1 0
Total Points Earned Total Points Available 18
Percentage
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