2. 5.3 Installment Purchases 1 Section 5.3 Installment Purchases (Amortization) Examples Butch

3. 5.3 Installment Purchases 2 I see how paying off a car loan is an example of recursion 1.Absolutely 2.Sort of 3.Not a clue Explain:

4. 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) 1. 3 – 4 years 2. 5 – 6 years 3. 7 – 8 years 4. 9 – 10 years 5. More

5. 5.3 Installment Purchases 4 Another Educated Guess ** Eventually, how much will Butch have to pay back to the bank? 1. The $12,000 he currently owes 2. The $12,000 + $216 3. The $12,000 + $2,160 4. The $12,000 + $12,160

6. 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) /. Amortize - defn

7. 5.3 Installment Purchases 6 The bank’s annual interest rate is 18% (= 0.18). What is its monthly rate? 1. 0.015 2. 0.15 3. 0.12 4. 0.18

8. 5.3 Installment Purchases 7 Jan 1 2007$12,000 Feb 1 2007 Mar 1 2007 Bank’s monthly interest % Jan. 1 $12,000 balance + - = Butch’s monthly payment $225 Feb 1 Balance ?

9. 5.3 Installment Purchases 8 Which of these recursion formulas would you use to compute Butch’s balance? (1.5% =.015) 1.Ans+.015*Ans-225 2.Ans+.015*Ans+225 3.Ans-.015*Ans-225 4.Ans-.015*Ans+225

10. 5.3 Installment Purchases 9 Use “Ans” to find Butch’s balance after 12 payments Butch owes $12,000 18% annual interest Monthly payment is $225 1. $7,591.62 2. $9,319.39 3. $11,413.15 4. $11,955.00

11. 5.3 Installment Purchases 10 Complete this “Amortization Schedule” Monthly Payment = $225 MonthBalanceBalance Bank (nearest cent) drops gets Jan$12,000 --- --- Feb$11,955. Mar.. Apr... June Answers

12. 5.3 Installment Purchases 11 Rule 1 Initially most of your monthly payment goes to the as interest goes to reduce your balance

13. 5.3 Installment Purchases 12 Which graph best describes Butch’s balance? 1.. 2.. 3.. 1.1 2.2 3.3 $ Years $ $

14. 5.3 Installment Purchases 13 Amortization (APPS) N Number of payments made – not years I%Annual interest rate – %, not a decimal PV Amount you owe – Enter as a (-) number PMT Periodic payment FVBalance after N payments P/Y Number of payments per year – Always 12 C/Y Number of compoundings per year – Always 12

15. 5.3 Installment Purchases 14 N = I% = PV = PMT = FV = P/Y = C/Y = “Butch Revisited” Verify balance = $11,413.15 after 1 year Owes $12,000 at 18% - Monthly payment = $225

16. 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”) 1. 6 years 2. 7 years 3. 8 years 4. 9 years 5. More

17. 5.3 Installment Purchases 16 How much will Butch have to pay back to the bank? 1. $12,000 + $123 2. $12,000 + $1,230 3. $12,000 + $12,300 4. $12,000 + $23,000

18. 5.3 Installment Purchases 17 Bank’s monthly interest + - = Butch’s monthly payment $400 0 ? … I think that I can squeeze out $400 a month 1. 30 months 2. 38 months 3. 38 years 4. 40 years

19. 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? 1. $2,400 2. $4,000 3. $5,400 4. $6,840 5. $12,300

20. 5.3 Installment Purchases 19 Rule 2 The your monthly payment, the you will pay off the loan, and the interest you will pay

21. 5.3 Installment Purchases 20 1. 66 months 2. 276 months 3. 276 years 4. He never will Bank’s monthly interest Jan. 1 $12,000 balance + - = Butch’s monthly payment $183 ? … I can only pay $183 a month. What me worry? 0

22. 5.3 Installment Purchases 21 Bank’s monthly interest Jan. 1 $12,000 balance + - = Butch’s monthly payment $175 0 ? … I can only pay $175 a month. Now I’m worried! 1. 131 months 2. 66 years 3. 276 years 4. He never will

23. 5.3 Installment Purchases 22 Why did you get an message in the last problem?

24. 5.3 Installment Purchases 23 Butch’s Summary Years To Total Interest Payment Pay Off Loan Paid $175.. $18323 years $50,508 $2259 years$12,300 $40040 months $4,000 $50030 months $3,000

25. 5.3 Installment Purchases 24 Rule 3 1.Make a payment each month, and 2.Make (A LOT) more than the minimum payment Always

26. 5.3 Installment Purchases 25 Credit Card Statement Minimum Payment Generally 2% of balance or $20, whichever is larger Applet

27. 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? 1.0 2.1 3.2 4.3 0 of 30 20000 Ans -.05*Ans + 212.13

28. 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? N = 3 I% =.05 PV = -212.13 PMT = 20000 FV = P/Y = 1 C/Y = 1 1.1 2.2 3.3 4.4 or more 0 of 30

29. 5.3 Installment Purchases 28 No $$$$$ ? + - = Monthly payment $175 0 1 year … Bank’s monthly interest 9% annual

30. 5.3 Installment Purchases 29 9% - payment = $175 - 1 year Cost of cruise? 1. $166 2. $1,253 3. $1,611 4. $2,001

31. 5.3 Installment Purchases 30 1.Dealership 2.Credit Union 3.Same $36,500 Better deal? DEALER I’ll knock $1,500 off the price and let you have it at 7.9% for 5 years CREDIT UNION I can’t reduce the price, but I’ll reduce the interest rate to 2.9% for 5 years

32. 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? 1. $107.61 2. $1,031.83 3. $1,670.95 4. $14,000.01

33. 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? 1.$348,330 2.$348,557 3.$349,212 4.$349,496

34. 5.3 Installment Purchases 33 2/28 A. R. M. #3: After two years the interest rate jumps to 10%. Your payments now are ? 1. $2,916.81 2. $2,996.17 3. $3,071.50

35. 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. $1,136 2. $1,231 3. $1,356

36. 5.3 Installment Purchases 35 End of 5.4

37. 5.3 Installment Purchases 36 Hello, Ma’am. I’m a college graduate selling vacuum cleaners to help pay for the fortune I borrowed to take courses that had nothing to do with selling vacuums. How are you? Installment Purchases

38. 5.3 Installment Purchases 37 How many credit cards and debit cards do you own? 1. 0 2. 1 - 3 3. 4 - 6 4. 7 or more

39. 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) 1. $0 (I pay it off each month) 2. Less than $200 3. Between $200 and $400 4. Between $400 and $600 5. Over $600

40. 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 1. $500 2. $1,000 3. $1,500 4. $2,000 5. $2,500

41. 5.3 Installment Purchases 40 Who pays your bill each month? 1. I do 2. Dad 3. Mom 4. Other

42. 5.3 Installment Purchases 41 What is the interest rate on your credit card? 1. 0 - 7% 2. 8 - 15% 3. 16 - 23% 4. Higher 5. Who knows?

43. 5.3 Installment Purchases 42 Reasons why credit cards are helpful

44. 5.3 Installment Purchases 43 Reasons why credit cards are dangerous

45. 5.3 Installment Purchases 44 Some Suggestions Pay bills off each month - NO interest charges Never miss a payment Copy your credit card account numbers and the telephone numbers of bank Call immediately if your card is lost/stolen Keep copies of sales slips and compare charges when your bills arrive

46. 5.3 Installment Purchases 45 $12,000 18% annual interest

47. 5.3 Installment Purchases 46 $12,180 $-225 $11,955 $12,000

48. 5.3 Installment Purchases 47 $-225 $11,909.33 $11,955 $12,134.33

49. 5.3 Installment Purchases 48 $-225 $11,862.96 $11,909.33 $12,087.96

50. 5.3 Installment Purchases 49 A - mortize To bring to Death

51. 5.3 Installment Purchases 50 Not to fear. It’s your bill that’s dying, not you Poof! $12,000

52. 5.3 Installment Purchases 51 Answers Monthly Payment = $225 MonthBalance Balance Bank dropsgets 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

53. 5.3 Installment Purchases 52 Consequences of making minimum paymentminimum

54. 5.3 Installment Purchases 53 Meta-Material