1. Copyright © Texas Education Agency, 2012. All rights reserved
Time Value of Money
A dollar in hand today is worth more than a dollar promised at some future time. Money is related to time.
Follow up on your statement that “A bird in the hand is worth two in the bush,” etc. and the answers to the students’ responses displayed, read the slide text. Say – “Suppose someone owed you $300. Would you rather have this money paid back now, in one payment, or later in installment payments? Does it make any difference?” Take a ‘vote’ from the class of those that think it DOES make a difference, and those that think it DOESN’T make any difference. Select a student that does not seem to be engaged in the lesson to write the results on the display board – whether it be an interactive whiteboard, dry erase board, or other.
“Time Value of Money”
MONEY MATTERS
Copyright © Texas Education Agency, All rights reserved

2. Copyright © Texas Education Agency, 2012. All rights reserved
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Follow up on your statement that “A bird in the hand is worth two in the bush,” etc. and the answers to the students’ responses displayed, read the slide text. Say – “Suppose someone owed you $300. Would you rather have this money paid back now, in one payment, or later in installment payments? Does it make any difference?” Take a ‘vote’ from the class of those that think it DOES make a difference, and those that think it DOESN’T make any difference. Select a student that does not seem to be engaged in the lesson to write the results on the display board – whether it be an interactive whiteboard, dry erase board, or other.
“Time Value of Money”
MONEY MATTERS
Copyright © Texas Education Agency, All rights reserved

3. Time Value of Money KEY TERMS
Bank
Opportunity Cost
Cash
Principal
Compound Interest
Reinvesting
Compounding
Savings
Decision
Savings Account
Interest
Simple Interest
Interest Rate
Trade-Off
Investing
Investment
Money
Allow students to read the terms. Solicit student input as you go over each term about what the terms mean. (Instruct that they will be responsible to the meaning of each term.) Tell students that you will be going over and explaining each one through the course of the lesson. Flip it positive and emphasize that you have already provided them with the list so they don’t even have to write it down! (At least not right now.)
“Time Value of Money”
MONEY MATTERS
Copyright © Texas Education Agency, All rights reserved

4. Principal (P)
the original amount invested to which interest is applied
Refer to the scenario presented in the lesson: “Suppose someone owed you $ ” – If someone PAID you $300 and you invested it in something – the $300 would be your principal. (Also point out that although this word is spelled the same as “Principal ??? (principal of your school)” – these are homonyms, and do not mean the same thing even though they are spelled the same and sound the same, they do not have the same meaning.)
Point out to students that principal is indicated with “P” in the formula to figure interest later in the lesson.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

5. Interest Rate (R)
the percentage that is used to calculate interest expressed as a fraction or decimal
Ask students if they have heard of interest rate. Since many are interested in buying their first car, they may have encountered the term while comparing car prices and loan terms. Tell students that the rate of interest is NOT the dollar amount of interest paid during the life of the loan and that you pay a little bit of interest each time you make a payment on a loan. At the end of the loan, the total interest paid is the result of the rate, but NOT the interest rate. Encourage them to make notes to this effect on their handout.
Emphasize to students that interest rate is represented by “R” in the formula to figure interest later in this lesson.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

6. Time Factor (T) the length of time for which interest will be charged
Ask students if they have heard any advertisements for car loans that specifically state 36 months or 60 months, etc. Allow them time to make comments regarding this. Tell them that these time increments mentioned are the time factor of a loan.
Point out that time factor is represented with “T” in the formula to figure interest later in the lesson.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

7. Simple Interest
Simple Interest – interest on an investment if not reinvested, so interest is earned each period on the original investment (principal) only
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

8. Investing for a Single Period – SIMPLE INTEREST
Formula
I (interest) = P (principal) x R (rate) x T (time)
Problem:
I = __?___
P-$100
R-10%
T-1 year)
Have students highlight the Formula for Simple Interest in their notes.
Discuss the components of the formula for simple interest.
Reiterate that interest rate is the percentage that is used to calculate interest expressed as a fraction or decimal. Be deliberate about discerning between Interest, which will be a dollar amount, and Interest RATE, which will be a percentage or decimal.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

9. Investing for a Single Period
$100 deposit into a savings account
10% interest rate per year annually)
?? How much will you have in
one year?
Reiterate that interest rate is the percentage that is used to calculate interest expressed as a fraction or decimal. Show students, through whiteboard, blackboard, etc. the equation for computing simple interest for 1 year.
Provide students with calculators to determine the answer.
Ask for a volunteer, or select a student , to write the formula for Simple Interest on your display media (whiteboard, dry erase, etc.). Have another student complete the equation using the numbers on this slide to determine the answer to the question.
Have students copy the formula for Simple Interest in their notes for this slide, then work with the student volunteer to figure the amount of interest at the end of one year using the calculator.
If need be use a document camera to go through the process on the calculator so students can follow.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

10. Investing for a Single Period – SIMPLE INTEREST (formula)
I (interest) = P (principal) x R (rate) x T (time)
In our situation:
(I = $10) = (P-$100) x (R-10%) x (T-1 year)
The display board should look like this when the student has completed the equation.
If not, redirect students to each component of the formula and how each item relates to the equation.
Check for understanding.
Work through the problem with and for any students who do not understand.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

11. Investing for a Single Period – SIMPLE INTEREST
I (interest) = P (principal) x R (rate) x T (time)
In our situation:
(I = $10) = (P-$100) x (R-10%) x (T-1 year)
Your investment has grown to $110!
(P = $100) + (I = $10) = $110
Ask students how much their investment has grown in the first year using simple interest.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

12. Reinvesting
Leaving principal and adding the interest to accumulate interest
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

13. Compounding
...the process of leaving an initial investment plus accumulated interest in a bank for more than one period
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

14. What if you leave that money in the bank?
What would you have after two (2) years, if the interest rate remains the same?
I (interest) = P (principal) x R (rate) x T (time)
(_______?) = P($110) x R (10%) x T (1 year)
Guide students through the formula for calculating the time value of the investment at the end of 2 years.
Call attention to the fact that whereas the original principal amount the first year was $100, with the added $10 interest earned, the principal has grown to $110.
Ask for a new student volunteer to complete the equation for Simple Interest for the second year.
Emphasize that instead of starting with only $100 this second year, they will start with $110 – which is how much their original investment grew, and that if they leave that money in the bank, they will be reinvesting.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

15. What if you leave that money in the bank?
I (interest) = P (principal) x R (rate) x T (time)
(I = _______?) = P($110) x R (10%) x T (1 year)
11 = $110 x 10% x 1 yr
Your investment has grown to $121!
(P = $110) + (I = $11) = $121
Guide students through the formula and process for calculating the time value of the investment at the end of 2 years.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

16. Compound Interest
Earning interest on interest through reinvesting. The result of compounding.
Refer back to slide 14 and show students the compound interest of $1 was interest earned the 2nd year on the $10 interest earned the 1st .
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

17. What if you leave that money in the bank?
Your investment has grown to $121!
(P = $110) + (I = $11) = $121
This $121 has four (4) parts:
$100 original principal
$10 interest earned the first year
$10 interest earned on principal the second year
$1 interest earned the second year on interest paid in the
first year (I first year = $10) x (R = 10%) = I second year $1
Guide students through the formula for calculating the compounded interest.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

18. Future Value
…cash value of an investment at a particular time in the future.
Future value refers to the amount of money to which an investment will grow over a finite period of time at a given interest rate. Consider a single-period investment.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

19. Future Value
What is the future value of the $100 principal at the end of two (2) years?
What was the amount of money to which the $100 investment would grow over two years at an interest rate of 10%?
Read the slide.
What was the amount of money to which the $100 investment would grow over two years at an interest rate of 10%?
Direct students’ attention to the display board (dry erase, etc.) where the student volunteer calculated the original simple interest equation.
Ask how much principal you started with at the beginning of the investment lesson. Answer - $100.
Ask how much the investment was worth at the end of two years. Answer $121.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

20. Investing for a Single Period – SIMPLE INTEREST
Formula
I (interest) = P (principal) x R (rate) x T (time)
Problem:
I = __?___
P-$100
R-10%
T-1 year)
Mention that this slide is the same as slide #7 you displayed earlier.
Point out that the original equation started out with $100 principal.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

21. What if you leave that money in the bank?
I (interest) = P (principal) x R (rate) x T (time)
(I = _______?) = P($110) x R (10%) x T (1 year)
11 = $110 x 10% x 1 yr
Your investment has grown to $121!
(P = $110) + (I = $11) = $121
Tell students that this slide is a copy of slide #14 from earlier.
This slide shows how the investment grew from $100 to $121 in two years.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

22. Opportunity Cost
The second-best alternative (or the value of that alternative) that must be given up when scarce resources are used for one purpose instead of another. The cost of any decision includes the cost of the best forgone opportunity.
Say – at the end of one year, the $100 principal had made $10 interest. Ask what else could have been done with the $10 interest that was earned?
Have a student volunteer make a list on the display of the items the students mention.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

23. Opportunity Cost What are some things you can do or buy with $10?
_______________________________
Have students brainstorm about what things they could do or buy with $10. THEN say – these are all opportunity costs. These are things that you would give up in order to leave the money in the bank to compound interest.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

24. Trade-Off
The giving up of one benefit or advantage in order to gain another regarded as more favorable. The trade-off between money now and money later depends on, among other things, the rate of interest you can earn by investing. The trade-off in our $100 investment grown to $121 is in all the things that were ‘given up’ in order to reinvest the original principal and the interest earned.
Emphasize that the trade-off is likened to opportunity cost. Emphasize (and read) “The trade-off in our $100 investment grown to $121 is in all the things that were ‘given up’ in order to reinvest the original principal and the interest earned.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

25. Opportunity Cost
The cost of any decision includes the cost of the best forgone opportunity
If you pay $10 for a movie ticket, your cost of attending the movie is not just the ticket price, but also the time and cost of what else you might have enjoyed doing instead of the movie. Applying this concept to the $300 owed you, you see that getting the money in installments will saddle you with opportunity cost. By taking the money over time, you lost the interest on your investment or any other use for the initial $300, such as spending it on something you would have enjoyed more.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

26. What Would YOU Do?
Suppose someone owed you $300. Would you rather have this money paid back now, in one payment, or later in installment payments? Does it make any difference?
According to a concept that economists call the time value of money, you would probably be better off getting your money right away, in one payment. You could invest this money and earn interest on it or you could use the money to pay off all or part of a loan. There are a million things you could do with this money.
Field comments and questions from the students on the questions:
Would you rather have the money now, or later in installments?
Does it make any difference?
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

27. Investing for a Single Period – SIMPLE INTEREST (formula)
I (interest) = P= $300 (principal) x R (rate) x T (time)
What would YOU do? Given the principal amount of $300, have students write a response to what they would do and why on paper and turn it in at the end of class.
Direct students to each component of the formula and how each item relates to the equation.
Have students complete the equation as they choose, then explain why they answered the question they way they did.
These responses are to be turned in for daily grade and check for understanding.
“Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved