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1.14.5<br />
<strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong><br />
Grade Level 9-12<br />
“Take Charge <strong>of</strong> Your Finances”<br />
<strong>Time</strong> to complete: 70 minutes<br />
National Content Standards<br />
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<br />
National Council on Economic Education Teaching Standards: 2, 3, 12<br />
National Standards for Business Education<br />
• Career Development:<br />
• Economics: IX.1<br />
• Personal Finance: IV.1, IV.2, VIII.1<br />
Objectives<br />
Upon completion <strong>of</strong> this lesson, students will be able to:<br />
• Understand the time value <strong>of</strong> money.<br />
• Understand how interest works.<br />
• Identify the components <strong>of</strong> a present and future value problem.<br />
• Use financial calculators to solve present and future value problems.<br />
• Define and use common terminology associated with savings and investing.<br />
Introduction<br />
One <strong>of</strong> the most amazing concepts about saving and investing is the time value <strong>of</strong> money. This means money paid<br />
out or received in the future is not equivalent to money paid out or received today. Essentially, the power <strong>of</strong> time is<br />
on a person’s side. There are three factors affecting how much an investment will grow: time, money, and interest<br />
rate. Interest rate is the percentage rate paid on the money invested or saved. The more an individual invests at a<br />
higher interest rate at an earlier age, the higher the future returns will be.<br />
Compounding vs. Simple Interest:<br />
Interest is the price <strong>of</strong> money. To understand how the future value <strong>of</strong> an investment works individuals must<br />
understand the difference between compounding and simple interest. Compounding interest is defined as earning<br />
interest on interest. It is the key concept to understanding the time value <strong>of</strong> money. Simple interest is interest<br />
earned on the principal investment. Principal refers to the original amount <strong>of</strong> money invested or saved.<br />
The following chart illustrates how compounding interest works.<br />
$1,000 Invested Compounded Monthly at 10% Interest Rate<br />
1 Year 2 Years 3 Years 4 Years 5 Years<br />
Total Return $1,104.71 $1,220.39 $1,348.18 $1,489.35 $1,645.31<br />
Interest earned and $104.71 $115.68 $127.79 $141.17 $155.96<br />
reinvested annually<br />
Total amount<br />
compounded monthly<br />
$1,000.00 $1,104.71 $1,220.39 $1,348.18 $1,489.35<br />
© Family Economics & Financial Education – Revised November 2004 – Saving Unit – <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> – Page 1<br />
Funded by a grant from Take Charge America, Inc. to the Norton School <strong>of</strong> Family and Consumer Sciences at the University <strong>of</strong> Arizona
1.14.5<br />
The equation for simple interest is:<br />
Interest earned = amount invested x the annual interest rate x the number <strong>of</strong> years.<br />
Therefore, if $1,000 was earning simple interest, multiplied by 10% interest, multiplied by 5 years the total would be<br />
$500 interest earned. Compounding interest earned $1,645.31 compared to $1,500 earned by simple interest.<br />
Three Factors Affecting the <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong>:<br />
<strong>Time</strong><br />
<strong>Time</strong> has an important impact <strong>of</strong> the future value <strong>of</strong> money. <strong>Time</strong> is referred to as “N,” or “number,” and signifies<br />
the number <strong>of</strong> times something happens to your money. For example, if a three year savings bond is compounded<br />
monthly, there would be 36 compounding periods (12*3). The earlier an individual invests, the more time their<br />
investment has to compound interest and increase in value. The “A Little Goes a Long Way” poster is a visual<br />
example <strong>of</strong> this. At 10% interest rate Sally Saver started investing $3,000 per year into an Individual Retirement<br />
Account at age 22 and invested a total <strong>of</strong> $30,000.00. Ed Uninformed began investing $3,000 per year into an<br />
Individual Retirement Account earning a 10% interest rate at age 28 and invested a total <strong>of</strong> $117,000.00. At age 65,<br />
when Ed and Sally would like to retire Sally has earned $1,239,564.00 from her $30,000 investment. Ed has earned<br />
$1,102,331.00 from his $117,000.00 investment.<br />
Interest Rate<br />
The higher the interest rate, the more money an individual will earn. Investments with interest rates compounding<br />
frequently will yield higher returns. However, an individual must understand an investment with a higher interest<br />
rate generally has a greater risk. Risk is the uncertainty the yield on an investment will deviate from what is<br />
expected. Having a savings or investment plan with a fixed interest rate (the rate will not change for the lifetime <strong>of</strong><br />
the investment) guarantees a specific return but can provide a moderate risk. If the average interest rates rise, the<br />
amount a person earns from this type <strong>of</strong> investment will not increase. Another consideration with interest rates is<br />
ensuring the interest rate is higher than the rate <strong>of</strong> inflation. Inflation is the steady rise in the general level <strong>of</strong> prices<br />
<strong>of</strong> a market basket <strong>of</strong> goods. If an individual has money invested at 4%, and the inflation rate is 4%, the individual<br />
wealth will not increase. In fact, after taxes they will actually be losing money.<br />
The following is an illustration <strong>of</strong> how interest rates affect the total return on $1,000.00:<br />
$1,000 Invested Compounded Monthly<br />
Interest Rate 1 Year 5 Years 10 Years<br />
4% $1,040.74 $1,221.00 $1,490.83<br />
6% $1,061.68 $1,348.85 $1,819.40<br />
8% $1,083.00 $1,489.85 $2,219.64<br />
10% $1,104.71 $1,645.31 $2,707.04<br />
Amount Invested<br />
Even if a person can only invest $50.00 per month, it is better than not investing anything at all. Developing a “Pay<br />
Yourself First” strategy is essential to a successful investment plan. Remember the 70-20-10 rule. Seventy percent<br />
can be spent, twenty percent should be saved, and 10 percent can be invested. To have money for savings and<br />
investing, individuals should evaluate their consumption habits. A person can earn thousands <strong>of</strong> dollars by<br />
decreasing the number <strong>of</strong> unnecessary purchases and investing that extra money. The Costs Add Up overhead<br />
1.14.4.D1 is provided to illustrate this point.<br />
© Family Economics & Financial Education – Revised November 2004 – Saving Unit – <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> – Page 2<br />
Funded by a grant from Take Charge America, Inc. to the Norton School <strong>of</strong> Family and Consumer Sciences at the University <strong>of</strong> Arizona
1.14.5<br />
<strong>Time</strong> <strong>Value</strong> Calculations – Future and Present <strong>Value</strong>:<br />
There are two types <strong>of</strong> time value calculations. The first is future value problems which the value <strong>of</strong> an asset is<br />
projected to the end <strong>of</strong> a particular time period. The second calculation is present value which is determining the<br />
current value <strong>of</strong> an asset received in the future. These calculations can easily be completed using a financial<br />
calculator. To understand what the calculator is doing, a person must understand the algebraic equations.<br />
Future <strong>Value</strong>:<br />
Present <strong>Value</strong>:<br />
FV = (PV )(1+i) N PV = (FV)(1+i) -N<br />
FV = Future <strong>Value</strong><br />
PV = Present <strong>Value</strong><br />
I = Interest Rate<br />
N = <strong>Time</strong>, the number <strong>of</strong> compounding periods<br />
In this lesson, students learn how to “make their money work for them” by learning about the future value <strong>of</strong> money.<br />
They will begin by comparing with classmates what they would do with $100.00. Next, the class will learn the<br />
difference between simple and compounding interest. This will be followed by a discussion on the three factors<br />
affecting the time value <strong>of</strong> money: time, interest rate, and amount invested. Finally, they learn the two equations<br />
(present value and future value) used to solve for the time value <strong>of</strong> money by using financial calculators.<br />
Body<br />
1. Provide each student with $100.00 in play money.<br />
a. Ask each student what they would do with the money.<br />
i. Record their answers on the board.<br />
ii. Appling the 70-20-10 Rule students will save $20.00 and invest $10.00.<br />
iii. The 70-20-10 Rule states for every dollar earned 70% can be spent, 20% should be saved,<br />
and 10% should be invested.<br />
b. Explain to them they will be learning about the <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong>. <strong>Money</strong> to be paid out or<br />
received in the future is not equivalent to money paid out or received today.<br />
c. The future value <strong>of</strong> money is how the adage “Make Your <strong>Money</strong> Work For You” was developed.<br />
i. This is because compounding interest causes money to make money.<br />
2. What causes the time value <strong>of</strong> money to grow is compounding interest.<br />
a. Compounding interest is earning interest on interest.<br />
b. This means if a person has $1000 earning 10% interest compounded annually he/she will earn<br />
$104.71 cents in interest. Therefore, in year two, it will be $1,104.71 earning 10% interest for a<br />
total <strong>of</strong> $1,220.39.<br />
c. Compounding interest is different than simple interest. Simple interest takes the amount invested<br />
multiplied by the annual interest rate multiplied by the number <strong>of</strong> years.<br />
3. Talk about the three factors affecting time value calculations.<br />
a. <strong>Time</strong> –<br />
i. The earlier a person can begin investing, the more return they will have in the future<br />
because the money has more time to work for them.<br />
ii. Show students the A Little Goes a Long Way poster 4.19.1 stressing how Sally only<br />
invested $30,000.00 and Ed invested $117,000.00 but Sally still earned more at retirement.<br />
iii. *Note to teacher – the interest rate is 10% because since the stock markets inception the<br />
average interest rate during any 25 year period has been 10%.<br />
b. Interest Rate<br />
i. Show The Importance <strong>of</strong> Interest Rates overhead 1.14.5.D3.<br />
ii. Stress the higher the interest rate, the greater the return on the investment.<br />
© Family Economics & Financial Education – Revised November 2004 – Saving Unit – <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> – Page 3<br />
Funded by a grant from Take Charge America, Inc. to the Norton School <strong>of</strong> Family and Consumer Sciences at the University <strong>of</strong> Arizona
1.14.5<br />
iii. However, higher interest rates generally mean a greater risk. Risk is the uncertainty the<br />
investment will not yield the amount expected.<br />
iv. Some investments have fixed rates (they will not change). However, this could be a risk<br />
because if average interest rates go up, the rates earned from the investment will not.<br />
v. Inflation is the steady rise in the general level <strong>of</strong> prices. If the interest rate for the savings or<br />
investment is not higher than inflation, a person will be losing money on an investment after<br />
taxes.<br />
c. Amount Invested<br />
i. The larger the amount invested the larger the return a person will earn.<br />
ii. Review the meaning <strong>of</strong> “Pay Yourself First.”<br />
1. Savings should be a fixed expense.<br />
iii. Review the 70-20-10 rule with students<br />
1. 70% can be spent, 20% saved, and 10% invested.<br />
iv. Show students the Costs Add Up overhead 1.14.5.D1. Talk to them about how they can<br />
personally decrease flexible expenses to increase the amount they are able to invest.<br />
v. Stress that every little bit helps. Even if a person can only save $1.00 per day it will add up.<br />
At 8% interest, invested at age 17, one dollar per day will become $17,865.52 by age 65.<br />
4. The two calculations used to figure the time value <strong>of</strong> money are future and present value calculations.<br />
a. They are algebraic equations students do not necessarily need to learn to solve in this class because<br />
financial calculators can calculate the answers.<br />
b. However, students do need to understand what the different components <strong>of</strong> the equations are.<br />
i. PV – Present <strong>Value</strong> (how much money does a person have today)<br />
ii. FV – Future <strong>Value</strong> (how much money does a person expect to have in the future)<br />
iii. i – Interest Rate<br />
iv. N – <strong>Time</strong> (calculated by the number <strong>of</strong> compounding periods: daily, monthly, or annually).<br />
c. *Note to teacher – to have the students practice using financial calculators using time value<br />
calculations, they may complete the Future <strong>Value</strong> Calculations lesson plan 1.6.2.<br />
5. Ask the students again what they would do with their $100.00.<br />
a. Record the answers on the board next to what was stated the first time.<br />
b. Show students the What Would You Do With $100.00 overhead 1.14.5.D2.<br />
c. Stress even a little saved early can compound into a lot by retirement.<br />
Conclusion<br />
Review with students the three factors influencing the time value <strong>of</strong> money: time, interest rate, and amount invested.<br />
Stress compounding interest is what “Makes Your <strong>Money</strong> Work for You.” It causes interest to earn additional<br />
interest rather than a person working to earn more money for investing. Finally, stress to students the value <strong>of</strong><br />
investing early.<br />
Assessment<br />
Have students complete the <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> Worksheet 1.14.5.A1.<br />
Materials<br />
<strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> Worksheet – 1.14.5.A1<br />
The Costs Add Up overhead – 1.14.5.D1<br />
What Would You Do With $100.00 overhead – 1.14.5.D2<br />
The Importance <strong>of</strong> Interest Rates overhead – 1.14.5.D3<br />
A Little Goes a Long Way Poster – 4.19.1<br />
© Family Economics & Financial Education – Revised November 2004 – Saving Unit – <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> – Page 4<br />
Funded by a grant from Take Charge America, Inc. to the Norton School <strong>of</strong> Family and Consumer Sciences at the University <strong>of</strong> Arizona
1.14.5<br />
Resources<br />
Family Economics & Financial Education Financial Calculators lesson plan 1.6.1<br />
Future <strong>Value</strong> Calculations 1.6.2<br />
• This lesson plan guides students through a series <strong>of</strong> future value problems using a financial calculator.<br />
American Express<br />
http://finance.americanexpress.com/fsc_ss/tools/retirement/waitcost.asp<br />
• This is a calculator from American Express. It demonstrates to students the difference in money earned<br />
by retirement if they wait to begin investing. In addition, there is another calculator which demonstrates<br />
to students how much they would earn if they reduced flexible expenses and invested the money.<br />
Financial Calculator<br />
http://www.hbcollege.com/finance/students/timevalue.htm<br />
• This is a great Web site containing a financial calculator for students.<br />
© Family Economics & Financial Education – Revised November 2004 – Saving Unit – <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> – Page 5<br />
Funded by a grant from Take Charge America, Inc. to the Norton School <strong>of</strong> Family and Consumer Sciences at the University <strong>of</strong> Arizona
1.14.5.A1<br />
Worksheet<br />
<strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> Worksheet<br />
Name_______________<br />
Total Points Earned<br />
16 Total Points Possible<br />
Percentage<br />
Date_______________<br />
Directions: Answer the following questions.<br />
1. What does the adage “Make Your <strong>Money</strong> Work For You” mean (1 point)<br />
2. What is the difference between compounding and simple interest (2 points)<br />
3. What are the three factors affecting time value <strong>of</strong> money calculations (3 points)<br />
4. Identify one thing people should know about when to begin investing. (1 point)<br />
5. Does a person want a higher or lower interest rate on an investment (1 point)<br />
6. What is the definition <strong>of</strong> risk (1 point)<br />
7. How do risk and interest rates relate to each other ( 1 point)<br />
8. What is the definition <strong>of</strong> inflation (1 point)<br />
9. Identify one example <strong>of</strong> how inflation affects an investment. (1 point)<br />
10. If a person only has $1.00 per day, or $30.00 per month, to invest, should he or she invest Why or<br />
why not (2 points)<br />
11. What are the two mathematical equations used for time value calculations ( 2 points)<br />
© Family Economics & Financial Education – Revised November 2004 – Saving Unit – <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> – Page 6<br />
Funded by a grant from Take Charge America, Inc. to the Norton School <strong>of</strong> Family and Consumer Sciences at the University <strong>of</strong> Arizona
1.14.5.D1<br />
Overhead<br />
The Costs Add Up<br />
The future value problems are calculated for an 18 year old person investing at 8% until age 65.<br />
Item Average Yearly Expense Future <strong>Value</strong><br />
Daily cup <strong>of</strong> c<strong>of</strong>fee at $2.50 $912.50 $38,704.46<br />
Eating lunch out 5 days per week<br />
at a cost <strong>of</strong> $5-$10 each time<br />
$1,300.00-$2,600.00 $55,140.60<br />
$110,281.21<br />
Daily can <strong>of</strong> soda or chips at $1.00<br />
each or both a can <strong>of</strong> pop and chips<br />
$365.00<br />
$730.00<br />
$15,481.78<br />
$30,963.57<br />
$2.00<br />
Daily candy bar at $1.00 $365.00 $15,481.78<br />
Daily can <strong>of</strong> chew or pack <strong>of</strong><br />
$1,383.35 $58,675.97<br />
cigarettes at $3.79<br />
Weekly attendance at a sporting<br />
$442.00 $18,747.81<br />
event at $3.50 admission and<br />
$5.00 for snacks<br />
Monthly hair cut at $25.00 per<br />
$300.00 $12,724.75<br />
month<br />
Monthly movie and popcorn for<br />
$240.00 $10,179.80<br />
two at $20.00<br />
Monthly cell phone plan at $35.00 $420.00 $17,814.66<br />
Monthly gym membership at<br />
$456.00 $19,341.63<br />
$38.00<br />
Driving a car 20 miles per day at<br />
.34 cents per mile to include gas,<br />
wear and tear, and maintenance<br />
(not including insurance or car<br />
payments)<br />
$2,482.00 $105,276.14<br />
© Family Economics & Financial Education – Revised November 2004 – Saving Unit – <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> – Page 7<br />
Funded by a grant from Take Charge America, Inc. to the Norton School <strong>of</strong> Family and Consumer Sciences at the University <strong>of</strong> Arizona
What Would You Do With $100.00<br />
If the students choose to invest the money into an account earning 8% interest compounded<br />
annually at age 17 and leave the money invested until age 65, they will earn $4,593.63.<br />
$100.00 Invested – 8% interest<br />
Age<br />
Amount Earned<br />
17 $100.00<br />
25 $189.25<br />
35 $420.06<br />
45 $932.38<br />
55 $2,069.54<br />
65 $4,593.63<br />
$4,593.63 Total Return From $100.00 Invested!!<br />
What if the student chooses to invest $30.00<br />
$30.00 Invested – 8% interest<br />
Age<br />
Amount Earned<br />
17 $30.00<br />
25 $56.77<br />
35 $126.02<br />
45 $279.71<br />
55 $620.86<br />
65 $1,378.09<br />
$1,378.09 Total Return from $30.00 Invested!!<br />
The <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong><br />
1.14.5.D2<br />
Overhead<br />
© Family Economics & Financial Education – Revised November 2004 – Saving Unit – <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> – Page 8<br />
Funded by a grant from Take Charge America, Inc. to the Norton School <strong>of</strong> Family and Consumer Sciences at the University <strong>of</strong> Arizona
1.14.5.D3<br />
Overhead<br />
The Importance <strong>of</strong> Interest Rates<br />
$1,000 Invested Compounded Monthly<br />
Interest Rate 1 Year 5 Years 10 Years<br />
4% $1,040.74 $1,221.00 $1,490.83<br />
6% $1,061.68 $1,348.85 $1,819.40<br />
8% $1,083.00 $1,489.85 $2,219.64<br />
10% $1,104.71 $1,645.31 $2,707.04<br />
12% $1,126.83 $1,816.70 $3,300.39<br />
At 4% interest, after 10 years,<br />
$1,490.83 is earned.<br />
At 12% interest, after 10 years,<br />
$3,300.39 is earned<br />
© Family Economics & Financial Education – Revised November 2004 – Saving Unit – <strong>Time</strong> <strong>Value</strong> <strong>of</strong> <strong>Money</strong> – Page 9<br />
Funded by a grant from Take Charge America, Inc. to the Norton School <strong>of</strong> Family and Consumer Sciences at the University <strong>of</strong> Arizona