The Secret to Becoming a Millionaire

Submitted by steciuma on Fri, 06/26/2009 - 2:54pm

Life Experience Connection:

Desire to become wealthy through investing.

Lesson Summary:

Students learn how saving helps people become wealthy. They develop “rules to become a millionaire” as they work through a series of activities. They learn that it is important to: 1) save early and often, 2) save as much as possible, 3) earn compound interest, 4) try to earn a high interest rate, 5) leave deposits and interest earned in the account as long as possible, and 6) choose accounts for which interest is compounded often. This lesson assumes that students have worked with percents and decimal equivalents. The time required for this lesson is 4-6 days.

Learning Objectives:

Students will be able to:

Define saving, incentive, interest, and opportunity cost.
Solve problems using interest rate, fractions, decimals, and percentages.
Calculate compound interest
Explain the benefits of compound interest
Explain the opportunity cost of saving
Describe a savings bond investment

Materials

Copies of Activities 1-1 through 1-5 for each student
Transparencies of Visuals 1-1 through 1-7
Calculator for each student
Computers
Transparency of opening question and The Advantage of Starting Early
Savings posters

Special notes/ideas:

Bring in savings account and investment ads; All parts of this lesson would not have to be used; A good deal of computation in this lesson; As compound interest gets broken down into smaller periods of time earned the lesson will get too involved for 6th grade; Opportunities for spreadsheets, graphing and writing in math; Can be used for enrichment/extension project.

Anticipatory Set:

1. Ask the following: Do you want to be a millionaire? What is a millionaire? Explain that a millionaire is a person who has wealth totaling one or more million dollars, noting that wealth is the total value of what a person owns minus what he or she owes. How could you become a millionaire? (win the lottery or a sweepstakes or a game show, inherit a million dollars, be a celebrity or pro sports athlete, earn a high income). Read the following scenario to the class:

Last week, Mrs. Addle told her students that they could become millionaires if they followed the rules she provided them. As a matter of fact, she guaranteed that if they followed her rules exactly, they would be millionaires in 47 years! Misha and the rest of her classmates thought that Mrs. Addle was crazy. If she had rules that would guarantee that someone could be a millionaire, why was she teaching seventh-grade math? Why wasn 't she rich and retired? Why didn 't she follow her own rules? Mrs. Addle told the students to go home and talk to their families about what she had said.

Misha went home and told her family what Mrs. Addle had said. Misha’s mother knew a lot about money and financial matters. She just smiled at Misha and said that Mrs. Addle was correct. When Misha returned to class the next day, Mrs. Addle asked what the students ' families said. Of the 25 students in Mrs. Addle's class, 20 students said that their parents and other family members agreed with Mrs. Addle. The other five students forgot to ask.

2. Explain that to learn more about being a millionaire, the students first must review what a percent is. (Note: If needed, Visual 1-1 includes a review.)

Point out that in the story, there are 25 students in Misha' s class, and 20 students discovered that their families agreed with Mrs. Addle. Ask the following questions. (Note: Step-by-step calculations are provided on Visual 1-2.)

What percent of the students' families thought that Mrs. Addle was correct? (80%)
b. What percent of the students failed to do their homework? (20%)

Instructional Plan Part 1

1. Explain that you will share Mrs. Addle's secrets with them. When they become millionaires, they can donate money to the school's math department! Discuss the following:

How do you earn income? (mow lawns, baby-sit, walk pets, rake leaves, do chores around the house)
What do you do with your income? (save it, spend it , save some' and spend some)
Why do you spend your income? (to buy things that they want now, such as movies, food, and clothes)
Why do you save your income? (to buy things they want in the future)

2. Explain that when people earn income, they can spend it or save it. When they are spending, they spend their money today for goods and services, but they give up the chance to have goods and services in the future. When saving, they give up goods and services now to have other goods and services in the future. When people make choices, the highest-valued alternative choice that is given up is their opportunity cost. Read the following scenario. [Use savings posters to get this point across to students].

Next year, you want to take a family and consumer science class, a woodworking class, and a photography class. However, you only have room in your schedule for one of these three. Which would you choose? What would be your second choice?

3. Have several students share their first and second choices. Explain that their second choice is their opportunity cost -- it is the highest-valued alternative class. When people save, the goods and services that they would have purchased now --- the highest-valued alternative -- represent their opportunity cost. When they spend now, their opportunity cost is goods and services they could have in the future.

4. Assign Activity 1-1. When they are finished, have students share answers. (1. $360, $720, $1080, $1440, $1800, $2160; 2. The items they would have purchased each day with $2. This is their opportunity cost. 3. A + (B x 180) where A = previous year balance and B = the amount deposited each day; 4. Save more each day.) Point out that students have different opportunity costs because their tastes and priorities are different.

5. Display Visual 1-3. Have students deduce what has changed in each case. They should deelop Rules 1 and 2 to become a millionaire. (In the first case, the saver is saving for a longer period, therefore, Millionaire Rule 1 is to start saving early. In the second case, the saver is saving $4 per day instead of $2 per day, therefore, Millionaire Rule 2 is to save more or to save as much as possible.) Write the two rules on the board.

6. Discuss the following:

How many of you have savings accounts in banks? (Answers will vary.)
What are the benefits of placing your savings in a bank? (The money is safe in the bank, and the bank pays interest.)
What is interest? (Students may or may not know the exact definition of interest.)

7. For homework, students who have savings accounts may bring in a statement from their savings accounts. Have all students look for ads in local newspapers and listen to television and radio ads about banks. Tell them to write down any information about interest rates.

Instructional Plan Part 2

1. Assign Activity 1-2. Allow students to share their answers. (1. $396, $831.60, $1310.76, $1837.84, $2417.62, $3055.38; 2. (A+360) -+- [0+360) x .10] where A is the previous year 's ending balance, or, 1.10 (A+360); 3. These amounts are higher because they earn interest on the deposit and interest on the interest earned in previous years.)

2. Point out that the 10% amount that Uncle Mort pays is an incentive. An incentive is a reward that encourages people to behave in a particular way. This incentive encourages people to save and keep their savings. How much of an incentive did Uncle Mort pay the first year? ($360 x .10 = $36)

3. Explain that banks provide an incentive for people to save. When people make deposits to savings accounts, banks are able to use the money to loan to others. In return, the banks pay interest to savers. Interest is a payment for the use of money. Bankers don't usually tell people that they will earn a specific sum of money. Savers are told the interest rate to be received. The interest rate is the annual interest payment on an amount expressed as a percentage. For example, a bank might pay a 4% interest rate on a savings account. Uncle Mort pays 10%.

4. Write the word "compounding" on the board. Ask students what they think this word means and how it applies to becoming a millionaire. Allow students to look the word up in the dictionary and in newspaper advertisements. Guide students to recognize that leaving interest earned on savings in the savings account so that the saver earns interest on the original deposit and interest on the interest is called earning compound interest. Have students develop Millionaire Rule 3 and write it on the board. (Earn compound interest.)

5. Explain that banks pay compound interest on savings, although it may not be as much as Uncle Mort pays. Discuss the following:

Give examples of the interest rates local banks are paying from the statements, ads, and ad information brought from home. (Answers will vary; however, the rates are likely to be much lower than the 10% that Uncle Mort pays.)
What would happen to the amount of accumulated savings if Uncle Mort paid only 5%? (It would decrease.)

6. Display Visual 1-4. Explain that this table illustrates what would happen if a bank paid 5% interest compounded annually. Point out that comparing the savings results at 5% with the savings results for 10% ($2571.12 at 5% compared to $3055.78 at 10%) gives us another rule for becoming a millionaire. Discuss the following:

Based on the comparison between accumulated savings with 5% interest and with 10% interest, what is the fourth rule of becoming a millionaire? (Try to earn a high interest rate.) Add this rule to the list on the board.
What would happen to accumulated savings if the deposits and interest were left in the account, earning 5% interest for another six years? (It would increase.)
What is the fifth rule of becoming a millionaire? (Leave deposits and interest in the account for as long as possible.) Add this rule to the board.

7.(optional) Have students consider how they used their calculators to solve these problems. Guide them to develop a recursive equation such as [ANS + 0.05(ANS)] = ending balance for each year or [ANS + 0.05(ANS)] + 360 = beginning balance for each successive year.

8. Review the basic rules for becoming a millionaire. Write the following rules on the board.

(1) Save early and often.
(2) Save as much as possible.
(3) Earn compound interest.
(4) Try to earn a high interest rate.
(5) Leave deposits and interest in the account as long as possible.

Instructional Plan 3 (Optional)

Tell students they will create four line graphs on the same set of axes. These graphs should show the amount of savings earned over time: (a) when saving $360 per year for six years in a bank, (b) when saving $360 for 10 years in a bank, (c) when saving $720 per year for six years, and (3) when saving $360 per year for six years at a 5% interest rate per year. They determine the dependent and independent variables and label the axes appropriately. They should retain these graphs for later use. They may use a graphing calculator, a computer, or paper and pencil to create the graphs.

Have students create a circle graph that shows the percent of total savings that resulted from deposits by the saver and the percent that resulted from compound interest when saving $360 per year for six years at a 5% interest rate. They may use a graphing calculator, a computer, or paper, pencil, and a protractor.

Assessment of Parts 1 and 2

Display Visual 1-4, and assign Activity 1-3 to each student. When students are finished, display Visual 1-5 so they can check their answers.

Instructional Plan Part 4

1. Have students refer to the savings account and advertisement information they brought from home. Discuss the following.

Do the ads or account statements tell consumers that the interest rate is compounded annually? Semi-annually? Quarterly? (Answers will vary.)
What do you think these terms mean? (annually - once per year; semi-annually - twice per year; quarterly - four times per year)
How do you think semi-annual or quarterly compounding might affect accumulated savings? (Answers may vary.)
How do you think quarterly interest payments would be calculated? (Answers may vary.)

2. Assign Activity 1-4 to groups of 4 or 5 students. Tell the groups to work together to complete the activity. Display Visual 1-6 to check and correct their answers.

3. Display Visual 1-4 again. Ask students to compare this table with the quarterly compound table they completed. Discuss the following.

What was the total amount deposited by the saver in each case? ($2160)
How much interest was earned with interest compounded annually? ($411.12)
How much interest was earned with interest compounded quarterly? ($419.54)
How much additional interest was earned through quarterly compounding? ($8.42)
What -do you think would happen if interest were compounded daily? (more accumulated savings at the end of the year)
What is the sixth and final rule for becoming a millionaire? (Deposit money in accounts for which interest is compounded most often.) Add the rule to the list on the board.

4. Review all rules to becoming a millionaire.

(1) Save early and often. (Show The Advantage of Starting Early overhead)
(2) Save as much as possible.
(3) Earn compound interest.
(4) Leave deposits and interest in the account for as long as possible.
(5) Try to earn high interest rates.
(6) Choose accounts for which interest is compounded often.

Discussion Questions for Students:

Discuss the following to highlight important information.

What does a percentage represent? (some part of a hundred)
How can 55% be expressed as a decimal? (.55) a fraction? (55/100)
What is interest? (payment for the use of money)
What is an interest rate? (the annual interest payment on an account expressed as a percentage)
What is compounding? (paying interest on previous interest)
What is saving? (income not spent today to be able to buy goods and services in the future)
What is opportunity cost? (the highest-valued alternative that is given up)
What is the opportunity cost of saving? (goods and services given up today)
What are some rules about saving that can help you become a millionaire? (Start saving early and save regularly. Save as much as you can. Leave the deposit and interest earned in the account as long as possible. Try to earn a high interest rate. Seek savings options that compound interest often.)

Group Writing Assessment

Explain that students' work with the computer or calculator helped them see the impact of the various rules on the quest to become a millionaire. Divide the students into small groups and tell them to answer the following questions in writing, as a group.

What happens to accumulated savings if the deposit amount increases? (Savings would increase. Saving larger amounts generates greater savings in the future. )
What happens to accumulated savings if the interest rate increases? (It would increase)
What happens to accumulated savings if the number of compounding periods per year increases? Why? (It would increase because every time compounding occurs, the saver is earning interest on interest earned )
What happens to accumulated savings if the number of years increases? (It would increase.)
What is the key to becoming a millionaire? (Save as much as possible for as long as possible earning a high interest rate that is compounded frequently.)

Extension Enrichment Activities

Activity One:

Remind students that one of the important rules about saving is to try to earn a high interest rate. To do that, savers must investigate various savings options available. If people save in a piggy bank, they don't earn any interest on their savings, and it isn't particularly safe. If people place their savings in a savings account at the bank, they earn interest and it is usually safe because of deposit insurance. However, the interest rate is usually lower on these accounts than some other savings options.
Explain that people can put their money in a certificate of deposit or CD. A certificate of deposit is a savings account that pays higher interest than a regular bank savings account. However, when people put their money in a CD, they promise to leave the savings in the account for a certain amount of time, such as six months, a year, or five years.
Explain that many people save by buying savings bonds issued by the United States government. When people buy a savings bond, they are lending money to the government to help finance programs or projects. Savings bonds come in different denominations, such as $50, $100, or $500. They are considered to be a very safe way to save money; that is, they are virtually risk-free.
Point out that the newest type of U.S. savings bond is the I Bond. I Bonds are inflation-indexed and designed for savers who want to protect themselves from inflation. Define inflation as an increase in the average level of prices in the economy. (A simpler definition is an increase in most prices.)
Explain that inflation reduces the purchasing power of savings. Purchasing power is the ability to buy things with an amount of money. People save because they want to buy things in the future. If they can buy a certain amount of things with $1000 today, people want to be able to buy at least the same things in the future with their savings. Discuss the following:
1. a. If you saved $1000 today to buy a $1000 computer next year, would you be able to buy it if your savings earned 5% and the price of the computer stayed the same? (Yes because you'd have approximately $1050 to buy the $1000 computer.)
2. b. If you saved $1000 today to buy a $1000 computer next year, would you be able to buy it if your savings earned 5% and the price of the computer increased 3%? (Yes because you'd have approximately $1050 to buy the computer that would cost $1030.)
3. c. If you saved $1000 today to buy a $1000 computer next year, would you be able to buy it if you savings earned 5% and the price of the computer increased 7%? (No because you'd have approximately $1050 to buy the computer that would cost $1070.)
Summarize by pointing out that inflation reduces the purchasing power of accumulated savings. If people's savings are going to have the same purchasing power in the future, then the interest/earnings on the savings must be equal to or greater than the inflation rate. For example, if the inflation rate is 4%, then the interest rate must be at least 4% so the saver could still be able to buy the same amount of things in the future with the money (principal).
Explain that this is exactly what the inflation-indexed I Bond is designed to do - protect the purchasing power of an individual's principal AND pay guaranteed earnings. The I Bond interest rate has two parts: a fixed interest rate that lasts for 30 years and an inflation rate that changes every six months if inflation changes. For example, an I Bond may pay a fixed interest rate of 4%. The semiannual inflation rate may be 2% for the first six months and 2.5% for the second half of the year. Therefore the combined interest rate would be 4% + 2% +2.5%.
Give each student a copy of Activity 1-5, and assign. Display Visual 1.7 to check answers.

Activity Two:

Divide the students into small groups. Assign each group a different savings instrument. For example, money market funds, treasury bonds, treasury bills, savings accounts, and certificates of deposits. Ask students to do some research to answer the following questions:

What is this savings instrument called?
Does it require a minimum balance?
Are there fees or penalties if you withdraw your money before a specified time?
Is this savings method more or less risky than savings bonds?
What is the interest rate on this savings instrument?
Is interest compounded annually, semi-annually, quarterly, daily?
How is the purchasing power of the savings protected from inflation?

Tell students that each group must prepare a brief presentation in which they compare the advantages and disadvantages of the savings instrument they choose with the advantages and disadvantages of an I Bond.

Additional Documents: