1. A dollar in hand today is worth more than a dollar promised at some future time. Money is related to time. 1 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

2. 2 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved “Copyright and Terms of Service Copyright © Texas Education Agency. The materials found on this website are copyrighted © and trademarked ™ as the property of the Texas Education Agency and may not be reproduced without the express written permission of the Texas Education Agency, except under the following conditions: 1)Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts’ and schools’ educational use without obtaining permission from the Texas Education Agency; 2) Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of the Texas Education Agency; 3) Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way; 4) No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged. Private entities or persons located in Texas that are not Texas public school districts or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside the state of Texas MUST obtain written approval from the Texas Education Agency and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty fee. Call TEA Copyrights with any questions you have.

3. Bank Cash Compound Interest Compounding Decision Interest Interest Rate Investing Investment Money Opportunity Cost Principal Reinvesting Savings Savings Account Simple Interest Trade-Off 3 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

4. Principal (P) the original amount invested to which interest is applied 4 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

5. Interest Rate (R) the percentage that is used to calculate interest expressed as a fraction or decimal 5 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

6. Time Factor (T) the length of time for which interest will be charged 6 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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 7 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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) 8 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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? 9 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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) 10 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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 11 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

12. Reinvesting Leaving principal and adding the interest to accumulate interest 12 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

13. Compounding...the process of leaving an initial investment plus accumulated interest in a bank for more than one period 13 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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) 14 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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 15 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

16. Compound Interest Earning interest on interest through reinvesting. The result of compounding. 16 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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: 1) $100 original principal 2) $10 interest earned the first year 3) $10 interest earned on principal the second year 4) $1 interest earned the second year on interest paid in the first year (I first year = $10) x (R = 10%) = I second year $1 17 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

18. Future Value …cash value of an investment at a particular time in the future. 18 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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%? 19 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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) 20 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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 21 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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. 22 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

23. Opportunity Cost What are some things you can do or buy with $10? 1. _______________________________ 2. _______________________________ 3. _______________________________ 4. _______________________________ 23 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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. 24 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

25. Opportunity Cost The cost of any decision includes the cost of the best forgone opportunity 25 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. 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? 26 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved

27. Investing for a Single Period – SIMPLE INTEREST (formula) I (interest) = P= $300 (principal) x R (rate) x T (time) 27 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, 2012. All rights reserved