section 4d loan payments, and credit cards pages 269-289 16

Section 4DSection 4DLoan Payments, and Credit Loan Payments, and Credit

CardsCards

Pages 269-289Pages 269-289

1616

Loan BasicsLoan Basics

The The principalprincipal is the amount of money is the amount of money owed at any particular time.owed at any particular time.

InterestInterest is charged on the loan principal. is charged on the loan principal.

1515

Month Month Prior Prior PrincipalPrincipal

InterestInterest1%1%

Payment Payment toward toward

PrincipalPrincipal

TotalTotal

PaymentPayment

New PrincipalNew Principal

11 $1200$1200 $12$12 $0$0 $12$12 $1200$1200

22 $1200$1200 $12$12 $0$0 $12$12 $1200$1200

33 $1200$1200 $12$12 $0$0 $12$12 $1200$1200

44 $1200$1200 $12$12 $0$0 $12$12 $1200$1200

55 $1200$1200 $12$12 $0$0 $12$12 $1200$1200

66 $1200$1200 $12$12 $0$0 $12$12 $1200$1200

pp269-270 Suppose you borrow $1200 at an annual interest rate of APR = 12%pp269-270 Suppose you borrow $1200 at an annual interest rate of APR = 12%Show the balance of the loan if you pay Show the balance of the loan if you pay only the interestonly the interest due for 6 months. due for 6 months.

BAD IDEABAD IDEA

1414

pg270 Suppose you borrow $1200 at an annual interest rate of APR = 12%pg270 Suppose you borrow $1200 at an annual interest rate of APR = 12%Show the balance of the loan if you pay Show the balance of the loan if you pay $200 toward principal plus interest$200 toward principal plus interest for 6 months.for 6 months.




PrincipalPrincipal

TotalTotal

PaymentPayment


11 $1200$1200 $12$12 $200$200 $212$212 $1000$1000

22 $1000$1000 $10$10 $200$200 $210$210 $800$800

33 $800$800 $8$8 $200$200 $208$208 $600$600

44 $600$600 $6$6 $200$200 $206$206 $400$400

55 $400$400 $4$4 $200$200 $204$204 $200$200

66 $200$200 $2$2 $200$200 $202$202 $0$0

VARYING PAYMENT AMOUNTSVARYING PAYMENT AMOUNTS

1313

pg270 Suppose you borrow $1200 at an annual interest rate of APR = 12%pg270 Suppose you borrow $1200 at an annual interest rate of APR = 12%Show the balance of the loan if you pay Show the balance of the loan if you pay $200$200 for 6 months. for 6 months.




PrincipalPrincipal

TotalTotal

PaymentPayment


11 $1200$1200 $12$12 $188$188 $200$200 $1012$1012

22 $1012$1012 $10.12$10.12 $189.88$189.88 $200$200 $822.12$822.12

33 $822.12$822.12 $8.22$8.22 $191.78$191.78 $200$200 $630.34$630.34

44 $630.34$630.34 $6.30$6.30 $193.70$193.70 $200$200 $436.64$436.64

55 $436.64$436.64 $4.37$4.37 $194.63$194.63 $200$200 $242.01$242.01

66 $242.01$242.01 $2.42$2.42 $197.58$197.58 $200$200 $44.43$44.43

increasingdecreasing

INSTALLMENT LOANINSTALLMENT LOAN

1212

Loan BasicsLoan Basics

The The principalprincipal is the amount of money is the amount of money owed at any particular time.owed at any particular time.

InterestInterest is charged on the loan principal. is charged on the loan principal.

To pay off a loan, you must gradually pay To pay off a loan, you must gradually pay down the principal. Each payment should down the principal. Each payment should include all the interest plus some amount include all the interest plus some amount that goes toward paying off the principal. that goes toward paying off the principal.

1111

Suppose you want to pay off a loan with regular Suppose you want to pay off a loan with regular (equal) monthly payments in a certain amount of (equal) monthly payments in a certain amount of time. Use Loan Payment Formula (pg 271)time. Use Loan Payment Formula (pg 271)

APR

PMT = ( )

APR 1 1 +

Pn

n Y

n

P = starting loan principal (amount borrowed)

PMT = equal regular payment

Y = loan term in years

n = number of payment periods per year

APR = annual percentage rate (as a decimal)

1010

pg270 Suppose you borrow $1200 at an annual interest rate of APR = 12%pg270 Suppose you borrow $1200 at an annual interest rate of APR = 12%How much should you pay each month in order to pay off the loan in 6 months.How much should you pay each month in order to pay off the loan in 6 months.

APR

PMT = ( )

APR 1 1 +

Pn

n Y

n

.121200

12PMT = ( 12 0.5)

.12 1 1 +

12

CALCULATORCALCULATOR

99

1200 .01PMT =

( 6) 1 1 + .01

12PMT = 1 .942045235

12PMT = .057954765

PMT = $207.06


88

The Loan Payment Formula (pg 271) can be used forThe Loan Payment Formula (pg 271) can be used for

• student loansstudent loans

• fixed rate mortgagesfixed rate mortgages

• credit card debtcredit card debt

• auto loansauto loans

More Practice . . .More Practice . . .

77

15*/26515*/265 A student loan of $25000 at a fixed APR of 10% for 20 years A student loan of $25000 at a fixed APR of 10% for 20 yearsa) Determine the monthly payment.a) Determine the monthly payment.b) Determine the total payment over the term of the loan.b) Determine the total payment over the term of the loan.c) Determine how much of the total payment over the loan termc) Determine how much of the total payment over the loan term goes to principal and how much to interest.goes to principal and how much to interest.

.1025000

12PMT = ( 12 20)

.10 1 1 +

12

= $241.26

Total Payment: 241.26 x 12 x 20 = Total Payment: 241.26 x 12 x 20 = $57902.40$57902.40

Principal Payment: Principal Payment: $25000$25000

Interest Payment: 57902.40 – 25000 =Interest Payment: 57902.40 – 25000 = $32902.40 $32902.40


66

35*/265 35*/265 A home mortgage of 100000 with a fixed APR of 8.5% for 30 years. A home mortgage of 100000 with a fixed APR of 8.5% for 30 years. a) Calculate the monthly payment.a) Calculate the monthly payment.b) Calculate the portions of the payments that go to principal and b) Calculate the portions of the payments that go to principal and to interest during the first 3 months. Use a table.to interest during the first 3 months. Use a table.

.085100000

12PMT = ( 12 30)

.085 1 1 +

12

= $768.91


InterestInterest0.7083%0.7083%


PrincipalPrincipal

TotalTotal

PaymentPayment


11 $100000$100000 $708.33$708.33 $60.58$60.58 $768.91$768.91 $99939.42$99939.42

22 $99939.42$99939.42 $707.90$707.90 $61.01$61.01 $768.91$768.91 $99878.41$99878.41

33 $99878.41$99878.41 $707.47$707.47 $61.44$61.44 $768.91$768.91 $99816.97$99816.97

55

29*/26529*/265 Suppose you have a credit card balance of $2500. The credit card Suppose you have a credit card balance of $2500. The credit card APR is 18% and you want to pay it off in 1 year. Determine the monthlyAPR is 18% and you want to pay it off in 1 year. Determine the monthly payment assuming you make no more credit card purchases.payment assuming you make no more credit card purchases.

.182500

12PMT = ( 12 1)

.18 1 1 +

12

= $229.20

Total Payment: 229.20 x 12 = Total Payment: 229.20 x 12 = $2750.40$2750.40

Principal Payment: Principal Payment: $2500$2500

Interest Payment: 2750.40 – 2500 =Interest Payment: 2750.40 – 2500 = $250.40 $250.40

44

37*/26537*/265 You need to borrow $10000 to buy a car and you determine that you can You need to borrow $10000 to buy a car and you determine that you canafford monthly payments of $220. The bank offers three choices: afford monthly payments of $220. The bank offers three choices:

a 3 year loan at 7%, a 3 year loan at 7%,

a 4 year loan at 7.5% or a 4 year loan at 7.5% or

a 5 year loan at 8%. a 5 year loan at 8%.

Which option is best for you?Which option is best for you?

$308.77

$241.79

$202.76

308.77 x 12 x 3 = $11115.79

241.79 x 12 x 4 = $11605.90

202.76 x 12 x 5 = $12165.60

33

Home Mortgages may be more complicated:Home Mortgages may be more complicated:

• interest rate (lower)interest rate (lower)

• down paymentdown payment

• closing costsclosing costs

•direct feesdirect fees

•points (each point is 1% of the loan amount)points (each point is 1% of the loan amount)

22

53/26553/265 You need a loan of $80000 to buy a home. In each of the two choices, You need a loan of $80000 to buy a home. In each of the two choices,calculate your monthly payments and total closing costs.calculate your monthly payments and total closing costs. Choice 1:Choice 1: 30 year fixed rate at 7.25% with closing costs of $1200 and 1 point. 30 year fixed rate at 7.25% with closing costs of $1200 and 1 point. Choice 2:Choice 2: 30 year fixed rate at 6.75% with closing costs of $1200 and 3 points. 30 year fixed rate at 6.75% with closing costs of $1200 and 3 points.

Choice Choice MonthlyMonthly

PaymentPayment

ClosingClosingCostCost

(direct)(direct)

Closing Closing CostCost

(points)(points)

TotalTotal

ClosingClosing

CostsCosts

TotalTotal

CostsCosts

11 $545.74$545.74 $1200$1200 $800$800 $2000$2000 196466 + 2000196466 + 2000

= $198466= $198466

22 $518.88$518.88 $1200$1200 $2400$2400 $3600$3600 186797 + 3600186797 + 3600

=$190397=$190397

.072580000

12PMT = ( 12 30)

.0725 1 1 +

12

.067580000

12PMT = ( 12 30)

.0675 1 1 +

12

11

Homework:Homework:

Pages 284-287Pages 284-287

#26, 36, 38, 40, 50, 54#26, 36, 38, 40, 50, 54

00

section 4d loan payments, and credit cards pages 269-289 16

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