5.3   Installment Purchases

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5.3 Installment Purchases

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1. 5.3 Installment Purchases 1 Cue applet on 29Cue applet on 29

2. 5.3 Installment Purchases 2 I see how paying off a car loan is an example of recursion Absolutely Sort of Not a clue

3. 5.3 Installment Purchases 3 Educated Guess ** How long it will take for Butch to pay-off his debt? (He borrows $12,000 for “new wheels” at 18% annual interest. He pays $225 monthly) 3 – 4 years 5 – 6 years 7 – 8 years 9 – 10 years More 44

4. 5.3 Installment Purchases 4 Another Educated Guess ** Eventually, how much will Butch have to pay back to the bank? The $12,000 he currently owes The $12,000 + $216 The $12,000 + $2,160 The $12,000 + $12,160 44

5. 5.3 Installment Purchases 5 Definition and Facts Your balance is . Interest rates are always for the year, but installment purchase accounts are compounded . Monthly interest rate = (Annual rate) / . How much you owe. 5-18% 12 monthlyHow much you owe. 5-18% 12 monthly

6. 5.3 Installment Purchases 6 The bank’s annual interest rate is 18% (= 0.18). What is its monthly rate? 0.015 0.15 0.12 0.18 44

7. 5.3 Installment Purchases 7 All by handAll by hand

8. 5.3 Installment Purchases 8 Which of these recursion formulas would you use to compute Butch’s balance? (1.5% = .015) Ans + .015*Ans - 225 Ans + .015*Ans + 225 Ans - .015*Ans - 225 Ans - .015*Ans + 225 11

9. 5.3 Installment Purchases 9 Use “Ans” to find Butch’s balance after 12 payments $7,591.62 $9,319.39 $11,413.15 $11,955.00 33

10. 5.3 Installment Purchases 10 Complete this “Amortization Schedule” Monthly Payment = $225 Month Balance Balance Bank (nearest cent) drops gets Jan $12,000 --- --- Feb $11,955 . Mar . . Apr . . . June New idea. Called an “amortization schedule” Students continue work from last slide to “see” Rule 1New idea. Called an “amortization schedule” Students continue work from last slide to “see” Rule 1

11. 5.3 Installment Purchases 11 Rule 1 Initially most of your monthly payment goes to the as interest goes to reduce your balance Bank / a much smaller amount From “Cabaret”Bank / a much smaller amount From “Cabaret”

12. 5.3 Installment Purchases 12 Which graph best describes Butch’s balance? 1 2 3 55

13. 5.3 Installment Purchases 13 Remind how to get into APPSRemind how to get into APPS

14. 5.3 Installment Purchases 14 “Butch Revisited” Verify balance = $11,413.15 after 1 year Owes $12,000 at 18% - Monthly payment = $225

15. 5.3 Installment Purchases 15 Under the same conditions ($12,000 at 18% paying $225 monthly) how long will it take Butch to pay off his loan? (Checking an earlier “guestimate”) 6 years 7 years 8 years 9 years More

16. 5.3 Installment Purchases 16 How much will Butch have to pay back to the bank? $12,000 + $123 $12,000 + $1,230 $12,000 + $12,300 $12,000 + $23,000 New technique required. APPS doesn’t helpNew technique required. APPS doesn’t help

17. 5.3 Installment Purchases 17 30 months 38 months 38 years 40 years 44

18. 5.3 Installment Purchases 18 Under these conditions ($12,000 at 18% paying $400 monthly), how much total interest will Butch pay over the life of the loan? $2,400 $4,000 $5,400 $6,840 $12,300 2 Real QED (400*#payments - 12000)2 Real QED (400*#payments - 12000)

19. 5.3 Installment Purchases 19 Rule 2 The your monthly payment, the you will pay off the loan, and the interest you will pay

20. 5.3 Installment Purchases 20 66 months 276 months 276 years He never will 3 = 23 years 3 = 23 years

21. 5.3 Installment Purchases 21 131 months 66 years 276 years He never will

22. 5.3 Installment Purchases 22 Why did you get an message in the last problem? QED discussionQED discussion

23. 5.3 Installment Purchases 23 Butch’s Summary Years To Total Interest Payment Pay Off Loan Paid $175 . . $183 23 years $50,508 $225 9 years $12,300 $400 40 months $4,000 $500 30 months $3,000

24. 5.3 Installment Purchases 24 Rule 3 Make a payment each month, and Make (A LOT) more than the minimum payment “Don’t You Mess with My Money” - Sterling Harrison“Don’t You Mess with My Money” - Sterling Harrison

25. 5.3 Installment Purchases 25 Credit Card Statement

26. 5.3 Installment Purchases 26 Good old Butch is at it again. He borrows $20,000 at 5% interest and has payments of $212.13. To find what his balance will be in three years he types in HOMESCREEN and presses ENTER 3 times. How many errors did he make? 0 1 2 3

27. 5.3 Installment Purchases 27 Butch keeps trying. He again borrows $20,000 at 5% interest and has payments of $212.13. To find his balance in 3 years he types these numbers in APPS. How many errors did he make this time?

28. 5.3 Installment Purchases 28 “Here Comes the Sun” - The Beatles“Here Comes the Sun” - The Beatles

29. 5.3 Installment Purchases 29 9% - payment = $175 - 1 year Cost of cruise? $166 $1,253 $1,611 $2,001 1. Solve for PV 1. Solve for PV

30. 5.3 Installment Purchases 30 Dealership Credit Union Same 2 “Shift Shifts and Safety Belts” - Cake2 “Shift Shifts and Safety Belts” - Cake

31. 5.3 Installment Purchases 31 “2/28 A. R. M.” (Adjustable Rate Mortgage) #1: You borrow $350,000 for 30 years to buy a home. Annual interest rate is 4%. Your monthly payment is? $107.61 $1,031.83 $1,670.95 $14,000.01 Subprime mortgage - 2 years fixed, 28 years variable Answer = $1,670.95 Subprime mortgage - 2 years fixed, 28 years variable Answer = $1,670.95

32. 5.3 Installment Purchases 32 “2/28 A. R. M.” #2: You borrow $350,000 at 4% interest for 30 years to buy a home. What is your balance after one month? $348,330 $348,557 $349,212 $349,496 $349,495.71$349,495.71

33. 5.3 Installment Purchases 33 2/28 A. R. M. #3: After two years the interest rate jumps to 10%. Your payments now are ? $2,916.81 $2,996.17 $3,071.50 Nice Problem: answer is $2,996.17 !!!! Careful: 10% mortgage is for 28 years Find FV for n = 24 ($337,421.63). Use this as PV. Make N = 28*12, and I = 10 and FV= 0. solve for PMT. Nice Problem: answer is $2,996.17 !!!! Careful: 10% mortgage is for 28 years Find FV for n = 24 ($337,421.63). Use this as PV. Make N = 28*12, and I = 10 and FV= 0. solve for PMT.

34. 5.3 Installment Purchases 34 Tuition for a 4-year university is now $22,218. It will increase by 5% annually. Your baby will enter college in 18 years. On that day you will put her first-year tuition bill on a credit card that charges 10% interest. You intend to pay it off monthly in 4 years. How much will each payment be? $1,136 $1,231 $1,356 Combo problem. Compound interest : tuition = $53,470 PMT = $1,346.14 Combo problem. Compound interest : tuition = $53,470 PMT = $1,346.14

35. 5.3 Installment Purchases 35 End of 5.4

36. 5.3 Installment Purchases 36 What do these five graphics have in common?What do these five graphics have in common?

37. 5.3 Installment Purchases 37 How many credit cards and debit cards do you own? 0 1 - 3 4 - 6 7 or more “Bills, Bills, Bills” - Beyonce“Bills, Bills, Bills” - Beyonce

38. 5.3 Installment Purchases 38 What is your average monthly credit card bill total for all your cards? (It’s the number at the bottom right-hand corner of your bill) $0 (I pay it off each month) Less than $200 Between $200 and $400 Between $400 and $600 Over $600

39. 5.3 Installment Purchases 39 Of those who carry a balance on their credit card each month, more than one-half have a balance above $500 $1,000 $1,500 $2,000 $2,500 Answer is 4. Actual answer is $1,800Answer is 4. Actual answer is $1,800

40. 5.3 Installment Purchases 40 Who pays your bill each month? I do Dad Mom Other

41. 5.3 Installment Purchases 41 What is the interest rate on your credit card? 0 - 7% 8 - 15% 16 - 23% Higher Who knows?

42. 5.3 Installment Purchases 42 Reasons why credit cards are helpful Emergencies Foreign travel Build a good credit ratingEmergencies Foreign travel Build a good credit rating

43. 5.3 Installment Purchases 43 Reasons why credit cards are dangerous Emergencies Foreign travel Build a good credit ratingEmergencies Foreign travel Build a good credit rating

44. 5.3 Installment Purchases 44

45. 5.3 Installment Purchases 45 ‘Satisfaction” – Rolling Stones‘Satisfaction” – Rolling Stones

46. 5.3 Installment Purchases 46

47. 5.3 Installment Purchases 47

48. 5.3 Installment Purchases 48

49. 5.3 Installment Purchases 49 A - “Darth Vader Death March”“Darth Vader Death March”

50. 5.3 Installment Purchases 50 Not to fear. It’s your bill that’s dying, not you

51. 5.3 Installment Purchases 51 Answers Monthly Payment = $225 Month Balance Balance Bank drops gets Jan $12,000 --- --- Feb $11,955 $45 $180 Mar $11,909.33 $45.67 $179.33 Apr $11,862.96 $46.37 $178.63 June $11,815.91 $47.05 $177.95 New idea. Called an “amortization schedule” Students continue work from last slide to “see” Rule 1New idea. Called an “amortization schedule” Students continue work from last slide to “see” Rule 1

52. 5.3 Installment Purchases 52 Consequences of making minimum payment In applet, choose “credit card” and then “credit card payoff” Can give term and payment. It will calculate payment for term you select and graph schedule. Then calculate time for payment you can make and graph this schedule Careful to zero “new charges” and “annual fee”In applet, choose “credit card” and then “credit card payoff” Can give term and payment. It will calculate payment for term you select and graph schedule. Then calculate time for payment you can make and graph this schedule Careful to zero “new charges” and “annual fee”

53. 5.3 Installment Purchases 53 Meta-Material

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