2. 5.2 Compound Interest 1 Recursion Chapter 5 Examples / “Snowball” / Definition

3. 5.2 Compound Interest 2 Section 5.2 Compound Interest Aunt Tilly / Recursion Machine

4. 5.2 Compound Interest 3 I see how compound interest is an example of recursion 1.Absolutely 2.Sort of 3.Not a clue Explain:

5. 5.2 Compound Interest 4 Take an educated guess Roughly how much will you have in 10 years? 1. $185,000 2. $200,000 3. $236,000 4. $260,000 5. $385,000

6. 5.2 Compound Interest 5 Definitions Interest Rate is Interest is Your account is Compounded Annually meaning Your Balance is

7. 5.2 Compound Interest 6 Calculate balance by hand Start 1 year later 2 years later 3 years later In general, Current Balance = Balance last year. Yugo

8. 5.2 Compound Interest 7 Here are the values we have: Jan 1 2008 $100000 Jan 1 2009 $110000 Jan 1 2010 $121000 Jan 1 2011 $133100 Homescreen on the TI “Ans” TI

9. 5.2 Compound Interest 8 Start with $100,000 at 10% interest. How much will you have at the end of 10 years? (nearest answer) 1. $185,000 2. $200,000 3. $236,000 4. $260,000 5. $385,000

10. 5.2 Compound Interest 9 Which graph best describes the growth of your balance? $ Years $ $ $ 1. 2. 3. 4. 1.1 2.2 3.3 4.4 Pots of Gold / Joke

11. 5.2 Compound Interest 10 With compound interest, the amount of interest you earn each year 1.Stays the same 2.Increases by the same amount 3.Increases by larger and larger amounts

12. 5.2 Compound Interest 11 Bad news: Hearing of Tilly’s sudden demise, her husband, Uncle Fester, unexpectedly passed on Good news: Annual COMPOUND interest 12% $200,000 Now Another sad story - Quiet please 15 years later ?

13. 5.2 Compound Interest 12 Suppose that after three years your balance is $280,986. Which expression gives your balance for the fourth year? 1. 280986 + 10000 2. 280986 + 12*280986 3. 280986 +.12 4. 280986 +.12*280986

14. 5.2 Compound Interest 13 Suppose that after three years your balance is $280,986. Which expression gives your interest for the fourth year? 1. 280986 + 12*280986 2. 280986 +.12*280986 3. 12*280986 4..12*280986

15. 5.2 Compound Interest 14 Your $200,000 is compounded annually at 12%. How much will you have at the end of 15 years? 1. $547,357 2. $835,450 3. $977,422 4. $1,094,713 5. $1,226,079

16. 5.2 Compound Interest 15 More Frequent Compounding

17. 5.2 Compound Interest 16 Complete the first column (red) of following chart assuming 12% interest Annual Semi-annual Quarterly Now$200,000 1 year later$224,000 2 years later 3 years later 4 years later$314,704

18. 5.2 Compound Interest 17 Your account at 12 % interest is compounded TWICE a year (July and January). What interest rate will be applied in July? 1. 1% 2. 5% 3. 6% 4. 12% 5. None of the above

19. 5.2 Compound Interest 18 Which is better? A.Receive 12% interest at the end of the year, or B.Receive % interest in July and another % interest the following January 1. A 2. B 3. Same

20. 5.2 Compound Interest 19 Why compounding twice a year is. than compounding annually (by hand)

21. 5.2 Compound Interest 20 $200,000 is invested at 12% interest compounded twice a year. What is your balance after 2 years? 1. $224,000 2. $250,880 3. $252,495 4. $275,865 5. None of the above

22. 5.2 Compound Interest 21 Now complete the second column (green) 12% interest Annual Semi-annual Quarterly Now$200,000 $200,000 1 year later$224,000$224,720 2 years later$250,880 3 years later$280,986 4 years later$314,704$318,770

23. 5.2 Compound Interest 22 April 1 January 1 Next year ? July 1 October 1 $200,000 January 1 Take things one step further 12% interest

24. 5.2 Compound Interest 23 $200,000 at 12% compounded quarterly for 1 year = ? 1. $220,763 2. $224,720 3. $225,102 4. $318,770 5. None of the above

25. 5.2 Compound Interest 24 Finally, complete the last column (blue) 12% interest Annual Semi-annual Quarterly Now$200,000 $200,000$200,000 1 year later$224,000$224,720$225,102 2 years later$250,880$252,495 3 years later$280,986$283,704 4 years later$314,704$318,770$320,941

26. 5.2 Compound Interest 25 Rule 1 The more times your account is compounded each year the more you earn

27. 5.2 Compound Interest 26 $200,000 at 12% compounded quarterly for 15 years. How many times must you press ENTER to get the answer? 1.15 2.30 3.45 4.60 5.None of the above

28. 5.2 Compound Interest 27 $200,000 at 12% compounded daily for 15 years. ( 365 days per year). How many times must you press ENTER to get the answer? 1.1585 2.5475 3.10575 4.More

29. 5.2 Compound Interest 28 You invest $1,000 at 12% interest compounded 12 times a year. Which of these recursion formulas would you not use to compute your balance? Aston - Martin 1.Ans + (.12/12)*Ans 2.Ans + (.1)*Ans 3.Ans + (12/12)*Ans 4.(.12/12)*Ans + Ans

30. 5.2 Compound Interest 29 Compound Interest Formulas (annual compounding)

31. 5.2 Compound Interest 30 Compound Interest in “APPS” N - The length of the account – in years I% - Annual interest rate as a percent, not a decimal PV - Deposit – negative number FV - Balance after N years C/Y - Times the account is compounded each year ALWAYS Set PMT = 0 – There are no payments Set P/Y = 1 Set the last line to END

32. 5.2 Compound Interest 31 Using “Ans” on HOMECREEN we saw that $200,000 at 12% compounded annually grew to $1,094,713 after 15 years - Verify this using “APPS” N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

33. 5.2 Compound Interest 32 $200,000 at 12% compounded daily for 15 years = ? 1. $1,199,160 2. $1,200,324 3. $1,205,876 4. $1,209,572 N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

34. 5.2 Compound Interest 33 “Maurice M. Barron” (March 8, 1997) I’m Peter Lynch with Fidelity. You’re right. Tell you what we’ll do. How about $105,000 to settle the matter? Hey Fidelity. What happened to my father’s money? In 1965 he invested $500 with you guys. It’s now 1997 and we haven’t heard a peep Just a minute. I took M116 at UH and remember some of this finance stuff. I’ll get back to you

35. 5.2 Compound Interest 34 1965 – 1997: $500 annual compounding at 22%. What would be a reasonable counter-offer? 1. $105,001.00 2. $237,752.32 3. $287,425.48 4. $290,057.82 5. $353,870.55 N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

36. 5.2 Compound Interest 35 A counter-offer based on daily compounding = ? 1. $105,002.00 2. $454,052.52 3. $564,858.76 4. $569,481.45 5. $569,484.76 6. $709,574.48 N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

37. 5.2 Compound Interest 36 Daily compounding - how much interest would the Barrons have earned just in the year 1997? 1. $91,234.97 2. $112,432.24 3. $457,052.52 4. $569,484.76 N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

38. 5.2 Compound Interest 37 “Bill and Melinda Gates” Hi Melinda. Tough day at the office? Not so bad. First thing this morning I took our $40 billion and invested it at 5% interest compounded daily. On the way home I withdrew the interest we made today Enough for dinner and a movie? Should cover it

39. 5.2 Compound Interest 38 How much interest did Bill and Melinda earn that day? $40 billion at 5% compounded daily for 1 day 1. $5,479 2. $5,618 3. $547,945 4. $5,479,452 5. $5,618,355 N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

40. 5.2 Compound Interest 39 What of these recursion formulas would you use to compute the Gates’ balance? 1.Ans + (.05/12)*Answer 2.Ans + (5/12)*Answer 3.Ans + (.05/365)*Answer 4.Ans + (0.5/365)*Answer 5.Ans + (5/365)*Answer

41. 5.2 Compound Interest 40 “Doubling Time” Start today at $40,000 Salary increases 7.18 % annually Years to double your salary? $80,000

42. 5.2 Compound Interest 41 How many years to double your salary? $40,000 at 7.18% annually 1. 10 years 2. 11 years 3. 13 years 4. 14 years N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

43. 5.2 Compound Interest 42 “ Gender Inequity” $30,000 $40,000 Men get 3% increase annually for 5 years % increase?

44. 5.2 Compound Interest 43 Men at $40K, Women at $30K. Over 5 years men get 3% increases. What % must women get to catch up? 1. 5.2% 2. 5.9% 3. 6.7% 4. 9.1% 5. 10.6% N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

45. 5.2 Compound Interest 44 “Good Old Days” Today’s (2008) tuition $26,942 1955 Tuition ? 5% increase annually

46. 5.2 Compound Interest 45 What was tuition in 1955? (Tuition today = $26,942, increased 3% annually) 1. $2,030 2. $3,145 3. $5,995 4. $7,455 N = I% = PV = PMT = 0 FV = P/Y = 1 C/Y =

47. 5.2 Compound Interest 46 End of 5.3

48. 5.2 Compound Interest 47 Recursion We can give you 12% interest if you never withdraw it I can’t take early retirement. I haven’t paid off my student loan yet ! If you miss a payment we show up and embarrass you in front of your friends

49. 5.2 Compound Interest 48 Snowball

50. 5.2 Compound Interest 49 Recursion? Recursion? What the heck is recursion? Ah! Here it is? re·cur·sion [ ri kúrzh'n ] noun ri kúrzh'n Early 17th c. "a running back" 1. The return to something repeatedly 2. Mathematics: the use of repeated steps, each based on the result of the one before to calculate a number

51. 5.2 Compound Interest 50 Thank you Thank you Thank you Her favorite niece/nephew $100,000 Dear Aunt Tilly

52. 5.2 Compound Interest 51 $100,000 10% annual COMPOUND interest

53. 5.2 Compound Interest 52 $133,100 $146,410 $121,000 4 years later1 year later 2 years later Now 3 years later Ok compound interest… Show me what you’ve got! $100,000 $110,000 10% compound interest

54. 5.2 Compound Interest 53 “HOMESCREEN” on the TI The YUGO of Methods Gets us there - Barely

55. 5.2 Compound Interest 54 $259,374 $100,000 $110,000 $121,000 $133,100 $146,410 10 years 10% interest

56. 5.2 Compound Interest 55 Math Joke (?) A dictionary definition Recursion: See Recursion

57. 5.2 Compound Interest 56 $200,000 Annual at 12% Semi-annual $1,094,713 Semi-annual at 12% $1,148,698 Semi-annual 15 years

58. 5.2 Compound Interest 57 “APPS” on the TI The “Aston Martin” of Methods Gets us there - Powerfully and in style

59. 5.2 Compound Interest 58 Meta – Material