Time Value of Money

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It is the key concept to understanding the time value of money. Simple interest is interest .... Directions: Answer the following questions. 1. What does the adage ...

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Time Value of Money Grade Level 9-12

“Take Charge of Your Finances” Time to complete: 70 minutes National Content Standards Family and Consumer Science Standards: 1.1.6, 2.1.2, 2.4.2, 2.5.1, 2.5.4, 2.6.1, 2.6.2, 3.3.2, 3.3.4 National Council on Economic Education Teaching Standards: 2, 3, 12 National Standards for Business Education • Career Development: • Economics: IX.1 • Personal Finance: IV.1, IV.2, VIII.1 Objectives Upon completion of this lesson, students will be able to: ƒ Understand the time value of money. ƒ Understand how interest works. ƒ Identify the components of a present and future value problem. ƒ Use financial calculators to solve present and future value problems. ƒ Define and use common terminology associated with savings and investing. Introduction One of the most amazing concepts about saving and investing is the time value of money. This means money paid out or received in the future is not equivalent to money paid out or received today. Essentially, the power of time is on a person’s side. There are three factors affecting how much an investment will grow: time, money, and interest rate. Interest rate is the percentage rate paid on the money invested or saved. The more an individual invests at a higher interest rate at an earlier age, the higher the future returns will be.

Compounding vs. Simple Interest: Interest is the price of money. To understand how the future value of an investment works individuals must understand the difference between compounding and simple interest. Compounding interest is defined as earning interest on interest. It is the key concept to understanding the time value of money. Simple interest is interest earned on the principal investment. Principal refers to the original amount of money invested or saved. The following chart illustrates how compounding interest works. $1,000 Invested Compounded Monthly at 10% Interest Rate 1 Year 2 Years 3 Years Total Return $1,104.71 $1,220.39 $1,348.18 Interest earned and $104.71 $115.68 $127.79 reinvested annually Total amount $1,000.00 $1,104.71 $1,220.39 compounded monthly

4 Years $1,489.35 $141.17

5 Years $1,645.31 $155.96

$1,348.18

$1,489.35

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money – Page 1 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona

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The equation for simple interest is: Interest earned = amount invested x the annual interest rate x the number of years. Therefore, if $1,000 was earning simple interest, multiplied by 10% interest, multiplied by 5 years the total would be $500 interest earned. Compounding interest earned $1,645.31 compared to $1,500 earned by simple interest.

Three Factors Affecting the Time Value of Money: Time Time has an important impact of the future value of money. Time is referred to as “N,” or “number,” and signifies the number of times something happens to your money. For example, if a three year savings bond is compounded monthly, there would be 36 compounding periods (12*3). The earlier an individual invests, the more time their investment has to compound interest and increase in value. The “A Little Goes a Long Way” poster is a visual example of this. At 10% interest rate Sally Saver started investing $3,000 per year into an Individual Retirement Account at age 22 and invested a total of $30,000.00. Ed Uninformed began investing $3,000 per year into an Individual Retirement Account earning a 10% interest rate at age 28 and invested a total of $117,000.00. At age 65, when Ed and Sally would like to retire Sally has earned $1,239,564.00 from her $30,000 investment. Ed has earned $1,102,331.00 from his $117,000.00 investment. Interest Rate The higher the interest rate, the more money an individual will earn. Investments with interest rates compounding frequently will yield higher returns. However, an individual must understand an investment with a higher interest rate generally has a greater risk. Risk is the uncertainty the yield on an investment will deviate from what is expected. Having a savings or investment plan with a fixed interest rate (the rate will not change for the lifetime of the investment) guarantees a specific return but can provide a moderate risk. If the average interest rates rise, the amount a person earns from this type of investment will not increase. Another consideration with interest rates is ensuring the interest rate is higher than the rate of inflation. Inflation is the steady rise in the general level of prices of a market basket of goods. If an individual has money invested at 4%, and the inflation rate is 4%, the individual wealth will not increase. In fact, after taxes they will actually be losing money. The following is an illustration of how interest rates affect the total return on $1,000.00: $1,000 Invested Compounded Monthly Interest Rate 1 Year 4% $1,040.74 6% $1,061.68 8% $1,083.00 10% $1,104.71

5 Years $1,221.00 $1,348.85 $1,489.85 $1,645.31

10 Years $1,490.83 $1,819.40 $2,219.64 $2,707.04

Amount Invested Even if a person can only invest $50.00 per month, it is better than not investing anything at all. Developing a “Pay Yourself First” strategy is essential to a successful investment plan. Remember the 70-20-10 rule. Seventy percent can be spent, twenty percent should be saved, and 10 percent can be invested. To have money for savings and investing, individuals should evaluate their consumption habits. A person can earn thousands of dollars by decreasing the number of unnecessary purchases and investing that extra money. The Costs Add Up overhead 1.14.4.D1 is provided to illustrate this point.

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money – Page 2 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona

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Time Value Calculations – Future and Present Value: There are two types of time value calculations. The first is future value problems which the value of an asset is projected to the end of a particular time period. The second calculation is present value which is determining the current value of an asset received in the future. These calculations can easily be completed using a financial calculator. To understand what the calculator is doing, a person must understand the algebraic equations. Future Value: FV = (PV )(1+i)N

Present Value: PV = (FV)(1+i)-N

FV = Future Value PV = Present Value I = Interest Rate N = Time, the number of compounding periods In this lesson, students learn how to “make their money work for them” by learning about the future value of money. They will begin by comparing with classmates what they would do with $100.00. Next, the class will learn the difference between simple and compounding interest. This will be followed by a discussion on the three factors affecting the time value of money: time, interest rate, and amount invested. Finally, they learn the two equations (present value and future value) used to solve for the time value of money by using financial calculators. Body 1. Provide each student with $100.00 in play money. a. Ask each student what they would do with the money. i. Record their answers on the board. ii. Appling the 70-20-10 Rule students will save $20.00 and invest $10.00. iii. The 70-20-10 Rule states for every dollar earned 70% can be spent, 20% should be saved, and 10% should be invested. b. Explain to them they will be learning about the Time Value of Money. Money to be paid out or received in the future is not equivalent to money paid out or received today. c. The future value of money is how the adage “Make Your Money Work For You” was developed. i. This is because compounding interest causes money to make money. 2. What causes the time value of money to grow is compounding interest. a. Compounding interest is earning interest on interest. b. This means if a person has $1000 earning 10% interest compounded annually he/she will earn $104.71 cents in interest. Therefore, in year two, it will be $1,104.71 earning 10% interest for a total of $1,220.39. c. Compounding interest is different than simple interest. Simple interest takes the amount invested multiplied by the annual interest rate multiplied by the number of years. 3. Talk about the three factors affecting time value calculations. a. Time – i. The earlier a person can begin investing, the more return they will have in the future because the money has more time to work for them. ii. Show students the A Little Goes a Long Way poster 4.19.1 stressing how Sally only invested $30,000.00 and Ed invested $117,000.00 but Sally still earned more at retirement. iii. *Note to teacher – the interest rate is 10% because since the stock markets inception the average interest rate during any 25 year period has been 10%. b. Interest Rate i. Show The Importance of Interest Rates overhead 1.14.5.D3. ii. Stress the higher the interest rate, the greater the return on the investment. © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money – Page 3 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona

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iii. However, higher interest rates generally mean a greater risk. Risk is the uncertainty the investment will not yield the amount expected. iv. Some investments have fixed rates (they will not change). However, this could be a risk because if average interest rates go up, the rates earned from the investment will not. v. Inflation is the steady rise in the general level of prices. If the interest rate for the savings or investment is not higher than inflation, a person will be losing money on an investment after taxes. c. Amount Invested i. The larger the amount invested the larger the return a person will earn. ii. Review the meaning of “Pay Yourself First.” 1. Savings should be a fixed expense. iii. Review the 70-20-10 rule with students 1. 70% can be spent, 20% saved, and 10% invested. iv. Show students the Costs Add Up overhead 1.14.5.D1. Talk to them about how they can personally decrease flexible expenses to increase the amount they are able to invest. v. Stress that every little bit helps. Even if a person can only save $1.00 per day it will add up. At 8% interest, invested at age 17, one dollar per day will become $17,865.52 by age 65. 4. The two calculations used to figure the time value of money are future and present value calculations. a. They are algebraic equations students do not necessarily need to learn to solve in this class because financial calculators can calculate the answers. b. However, students do need to understand what the different components of the equations are. i. PV – Present Value (how much money does a person have today) ii. FV – Future Value (how much money does a person expect to have in the future) iii. i – Interest Rate iv. N – Time (calculated by the number of compounding periods: daily, monthly, or annually). c. *Note to teacher – to have the students practice using financial calculators using time value calculations, they may complete the Future Value Calculations lesson plan 1.6.2. 5. Ask the students again what they would do with their $100.00. a. Record the answers on the board next to what was stated the first time. b. Show students the What Would You Do With $100.00 overhead 1.14.5.D2. c. Stress even a little saved early can compound into a lot by retirement. Conclusion Review with students the three factors influencing the time value of money: time, interest rate, and amount invested. Stress compounding interest is what “Makes Your Money Work for You.” It causes interest to earn additional interest rather than a person working to earn more money for investing. Finally, stress to students the value of investing early. Assessment Have students complete the Time Value of Money Worksheet 1.14.5.A1. Materials Time Value of Money Worksheet – 1.14.5.A1 The Costs Add Up overhead – 1.14.5.D1 What Would You Do With $100.00? overhead – 1.14.5.D2 The Importance of Interest Rates overhead – 1.14.5.D3 A Little Goes a Long Way Poster – 4.19.1 © Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money – Page 4 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona

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Resources Family Economics & Financial Education Financial Calculators lesson plan 1.6.1 Future Value Calculations 1.6.2 ƒ This lesson plan guides students through a series of future value problems using a financial calculator. American Express http://finance.americanexpress.com/fsc_ss/tools/retirement/waitcost.asp ƒ This is a calculator from American Express. It demonstrates to students the difference in money earned by retirement if they wait to begin investing. In addition, there is another calculator which demonstrates to students how much they would earn if they reduced flexible expenses and invested the money. Financial Calculator http://www.hbcollege.com/finance/students/timevalue.htm ƒ This is a great Web site containing a financial calculator for students.

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money – Page 5 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona

1.14.5.A1 Worksheet

Time Value of Money Worksheet Name_______________ Date_______________ 16

Total Points Earned Total Points Possible Percentage

Directions: Answer the following questions. 1. What does the adage “Make Your Money Work For You” mean? (1 point) 2. What is the difference between compounding and simple interest? (2 points)

3. What are the three factors affecting time value of money calculations? (3 points)

4. Identify one thing people should know about when to begin investing. (1 point) 5. Does a person want a higher or lower interest rate on an investment? (1 point) 6. What is the definition of risk? (1 point)

7. How do risk and interest rates relate to each other? ( 1 point) 8. What is the definition of inflation? (1 point) 9. Identify one example of how inflation affects an investment. (1 point)

10. If a person only has $1.00 per day, or $30.00 per month, to invest, should he or she invest? Why or why not? (2 points)

11. What are the two mathematical equations used for time value calculations? ( 2 points)

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money – Page 6 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona

1.14.5.D1 Overhead

The Costs Add Up The future value problems are calculated for an 18 year old person investing at 8% until age 65.

Item Daily cup of coffee at $2.50 Eating lunch out 5 days per week at a cost of $5-$10 each time Daily can of soda or chips at $1.00 each or both a can of pop and chips $2.00 Daily candy bar at $1.00 Daily can of chew or pack of cigarettes at $3.79 Weekly attendance at a sporting event at $3.50 admission and $5.00 for snacks Monthly hair cut at $25.00 per month Monthly movie and popcorn for two at $20.00 Monthly cell phone plan at $35.00 Monthly gym membership at $38.00 Driving a car 20 miles per day at .34 cents per mile to include gas, wear and tear, and maintenance (not including insurance or car payments)

Average Yearly Expense $912.50 $1,300.00-$2,600.00 $365.00 $730.00

Future Value $38,704.46 $55,140.60 $110,281.21 $15,481.78 $30,963.57

$365.00 $1,383.35

$15,481.78 $58,675.97

$442.00

$18,747.81

$300.00

$12,724.75

$240.00

$10,179.80

$420.00 $456.00

$17,814.66 $19,341.63

$2,482.00

$105,276.14

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money – Page 7 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona

1.14.5.D2 Overhead

What Would You Do With $100.00? If the students choose to invest the money into an account earning 8% interest compounded annually at age 17 and leave the money invested until age 65, they will earn $4,593.63.

$100.00 Invested – 8% interest Age 17 25 35 45 55 65

Amount Earned $100.00 $189.25 $420.06 $932.38 $2,069.54 $4,593.63

$4,593.63 Total Return From $100.00 Invested!! What if the student chooses to invest $30.00?

$30.00 Invested – 8% interest Age 17 25 35 45 55 65

Amount Earned $30.00 $56.77 $126.02 $279.71 $620.86 $1,378.09

$1,378.09 Total Return from $30.00 Invested!!

The Time Value of Money

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money – Page 8 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona

1.14.5.D3 Overhead

The Importance of Interest Rates

$1,000 Invested Compounded Monthly Interest Rate 1 Year 5 Years 4% $1,040.74 $1,221.00 6% $1,061.68 $1,348.85 8% $1,083.00 $1,489.85 10% $1,104.71 $1,645.31 12% $1,126.83 $1,816.70

10 Years $1,490.83 $1,819.40 $2,219.64 $2,707.04 $3,300.39

At 4% interest, after 10 years, $1,490.83 is earned. At 12% interest, after 10 years, $3,300.39 is earned

© Family Economics & Financial Education – Revised November 2004 – Saving Unit – Time Value of Money – Page 9 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona