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

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:

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

5.3 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 + $ The $12,000 + $2, The $12,000 + $12,160

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

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

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

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 Ans+.015*Ans Ans-.015*Ans Ans-.015*Ans+225

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 $ $7, $9, $11, $11,955.00

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

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

5.3 Installment Purchases 12 Which graph best describes Butch’s balance? $ Years $ $

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

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

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

5.3 Installment Purchases 16 How much will Butch have to pay back to the bank? 1. $12,000 + $ $12,000 + $1, $12,000 + $12, $12,000 + $23,000

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 months months years years

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, $4, $5, $6, $12,300

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

5.3 Installment Purchases months months 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

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! months years years 4. He never will

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

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

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

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

5.3 Installment Purchases 26 Good old Butch is at it again. He borrows $20,000 at 5% interest and has payments of $ 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? of Ans -.05*Ans

5.3 Installment Purchases 27 Butch keeps trying. He again borrows $20,000 at 5% interest and has payments of $ 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 = PMT = FV = P/Y = 1 C/Y = or more 0 of 30

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

5.3 Installment Purchases 29 9% - payment = $ year Cost of cruise? 1. $ $1, $1, $2,001

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

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. $ $1, $1, $14,000.01

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

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, $2, $3,071.50

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, $1, $1,356

5.3 Installment Purchases 35 End of 5.4

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

5.3 Installment Purchases 37 How many credit cards and debit cards do you own? or more

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 $ Between $200 and $ Between $400 and $ Over $600

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. $ $1, $1, $2, $2,500

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

5.3 Installment Purchases 41 What is the interest rate on your credit card? % % % 4. Higher 5. Who knows?

5.3 Installment Purchases 42 Reasons why credit cards are helpful

5.3 Installment Purchases 43 Reasons why credit cards are dangerous

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

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

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

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

5.3 Installment Purchases 48 $-225 $11, $11, $12,087.96

5.3 Installment Purchases 49 A - mortize To bring to Death

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

5.3 Installment Purchases 51 Answers Monthly Payment = $225 MonthBalance Balance Bank dropsgets Jan$12, Feb$11,955 $45$180 Mar$11, $45.67$ Apr$11, $46.37$ June$11, $47.05$177.95

5.3 Installment Purchases 52 Consequences of making minimum paymentminimum

5.3 Installment Purchases 53 Meta-Material