INSTALLMENT BUYING AND REVOLVING CHARGE CREDIT

CARDSChapter Ten

Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

1. Calculate the amount financed, finance charge, and deferred payment.

2. Calculate the APR.3. Calculate the monthly payment.

LU 10-1: Cost of Installment Buying

LEARNING UNIT OBJECTIVES

LU 10-2: Revolving Charge Credit Cards

1. Calculate the finance charges on revolving charge credit card accounts.

10-2

Finance charge (FC) –

the interest charge.

FC = Total of all -- Amount

monthly payments financed

Installment loan –

A loan paid off in a series of equal periodic payments.

Payments include interest and principal.

Amount financed (AF) –

the amount actually borrowed.

AF = Cash price -- Down payment

Deferred payment price (DPP) –

the total of all monthly payments plus the down payment.

DPP = Total of all + Down

monthly payments payment

COST OF INSTALLMENT BUYING

10-3

COST OF INSTALLMENT BUYING

Mary Wilson would like to buy a truck that cost $9,345. If she puts down $300 she can finance the balance for 60 months at 10.5% (monthly payment = $194.38). Calculate the amount financed, finance charge, and deferred payment price.

Amount financed = Cash price -- Down payment

Finance charge = Total of all -- Amount monthly payments financed

Deferred payment price = Total of all + Down

monthly payments payments10-4

$9,045 = $9,345 -- $300

$2,617.80 = $11,662.80 -- $9,045 ($194.38 x 60)

$11,962.80 = $11,662.80 + $300 ($194.38 x 60)

TRUTH IN LENDING: (APR) DEFINED AND CALCULATED

Truth in

Lending Act

APR must be

accurate to

the nearest

1/4 of 1%

10-5

The APR represents the true or effective annual interest creditors charge.

The Truth in Lending Act requires creditors provide in writing the amount of the finance charge and the annual percentage rate (APR).

CALCULATING APR BY FORMULA

APR = 72 x I3P(N + 1) + I(N – 1)

WhereI = Finance charge on the loanP = Amount financedN = Number of months of the loan

Now let’s determine the APR for the pickup truck advertisement given earlier in the chapter.

APR = 72 x I3P(N + 1) + I(N – 1)

APR = 72 X $2,617.803($9,045)(60 + 1) + $2,617.80(60 – 1)

10-6

= $188,481.60 $1,655,235 + $154,450.20

CALCULATING APR BY FORMULA

APR = $188,481.60 $1,809,685.20

= .1041516 = 10.4% APR, roughly

72 x 2,617.80 = STO 1 3 x 9,045 x 61 = STO 2

2,617.80 x 59 = RCL 2 = STO 2 RCL 1 ÷ RCL 2 = .10415

CALCULATOR STEPS

10-7

Clear the TVM register each time you work with the new data by pressing [2ND] [CLR TVM].

You can enter the variables into the calculator in any order: Enter 0 for any unused variable in a worksheet.

Enter money paid as a negative number by using the +/- after entering the number. For example, entering 432 [+/-] gives -432.

Enter money received as a positive number.Enter the I/Y (interest rate per year) variable as a

periodic rate. This key has already been programmed to recognize percents. For example, 10% would be entered simply as 10 or .833333333 for 10%/12.

Keep in mind there may be rounding diff erences when calculating the answer using diff erent methods.

TI BA II PLUS CALCULATOR

10-8

Pressing 2ND allows you to access the function listed above each key. These functions are shown in brackets, such as [FORMAT]. Format is the secondary function above the decimal point key.

Make certain the number of decimal places shown is 9 by pressing 2ND [FORMAT] 9 [ENTER]. Note: Anytime you reset your calculator, you must format the decimal places to 9 again.

TI BA II PLUS CALCULATOR

10-9

Step 1. Enter the number of periods and press N.Step 2. Enter the loan amount and press PV.Step 3. Enter payment amount, +|-, and press FV.Step 4. Enter 0 for the future value and press FV.Step 5. Press CPT I/Y x 12 to obtain the annual rate.

CALCULATING APR BY FINANCIAL CALCULATOR WHEN MONTHLY PAYMENT

IS KNOWN

10-10

Example: Use the pickup truck advertisement given earlier in the chapter. First let’s clear the time-value-of-money register by pressing [2ND] [CLR TVM]. Now we enter these values:Step 1. 60 NStep 2. 9,045 PVStep 3. -194.38 PMTStep 4. 0 FVStep 5. [CPT] [I/Y] x 12

Step 1. Calculate the periodic rate in decimal format.Step 2. Substitute values for N, i, and PV into the formula.Step 3. Solve.

CALCULATING THE MONTHLY PAYMENT BY FORMULA

10-11

PMT = PV(i)

1 – 1 (1 + i)N

N = number of paymentsi = periodic interest ratePV = loan amountPMT = monthly payment

EXAMPLE:

PMT = $9,045(.00875)1 – 1 (1 + .00875)60

1 – 1 (1.686602982)

PMT = $79.14375 = $79.143751 - .592907762

= $79.14375PMT

.407092238= $194.41

10.5%/12 =.875% =.00875

CALCULATING THE MONTHLY PAYMENT USING CALCULATOR

9,045 x .00875 = STO 1 (1 + .00875) yx 60 = STO 2

1 ÷ RCL 2 = STO 2 1 – RCL 2 = STO 2 RCL 1 ÷ RCL 2 = 194.41

10-12

Step 1. Enter the number of periods and press N.Step 2. Enter I/12 to find the monthly periodic rate.Step 3. Enter the loan amount and press PV.Step 4. Enter 0 for the future value and press FV.Step 5. Press CPT PMT.

CALCULATING MONTHLY PAYMENT BY FINANCIAL

CALCULATOR

10-13

Using our truck example again:Step 1. 60 NStep 2. 10.5/12 = iStep 3. 9,045 PVStep 4. 0 FVStep 5. CPT PMT -194.41

Step 1. Calculate the monthly payment for the amount financed. Enter N, PV, and I/Y as i/12 to obtain the monthly periodic rate. Then, press CPT PMT.

Step 2. Subtract the loan charges from the loan amount (PV) and solve for i by recalculating I/Y using the same N, PV, and PMT (calculated in Step 1).

Step 3. Multiply the interest rate you found in Step 2 by 12 for an annual rate.

CALCULATING APR ON LOAN WITH LOAN CHARGES

10-14

Step 1. Calculate the monthly payment for the amount financed. Enter N, PV, and I/Y as i/12 to obtain the monthly periodic rate. Then, press CPT PMT.

CALCULATING APR ON LOAN WITH LOAN CHARGES

10-15

EXAMPLECarla Malmquist got a screaming deal on a 2013 Lexus IS C. She financed $49,500 at 2% for 5 years. The $49,500 financed included loan charges of $450.

Step 1. 60 NStep 2. 49,500 PVStep 3. 2/12 = iStep 4. 0 FVStep 5. CPT PMT -867.62

Step 2. Subtract the loan charges from the loan amount (PV) and solve for i by recalculating I/Y using the same N, PV, and PMT (calculated in Step 1).

CALCULATING MONTHLY PAYMENT BY FINANCIAL

CALCULATOR

10-16

$49,500 - $450 = $49,050 net proceeds

Step 1. 60 NStep 2. 867.62 +|- PMTStep 3. 49,050 PVStep 4. 0 FVStep 5. CPT I/Y x 12 2.37%

Step 3. Multiply the interest rate you found in Step 2 by 12 for an annual rate.

Step 1. Calculate interest: Principal x Rate x Time.Step 2. Add interest calculated in Step 1 to amount financed (principal).Step 3. Calculate the monthly payment by dividing Step 2 by N

using your calculator.Step 4. Enter the number of periods and press N.Step 5. Enter the loan amount and press PV.Step 6. Enter payment amount, +|-, and press PMT.Step 7. Enter 0 for the future value and press FV.Step 8. Press CPT I/Y x 12.

CALCULATING APR BY THE ADD-ON METHOD

10-17

CALCULATING APR BY THE ADD-ON METHOD

EXAMPLE Calculate the APR using the add-on method for the following loan: $5,450 at 8% for 48 months.

Steps 1 - 3.

I = PRT

I = $5,450 x .08 x 4I = $1,744

$5,450 + $1,744 = $7,194$7,194/48 = $149.88 monthly payment

Steps 4 - 8.Step 4. 48 NStep 5. 5,450 PVStep 6. 149.88 +|- PMTStep 7. 0 FVStep 8. CPT I/Y x 12 14.3%

10-18

PAYING JUST THE MINIMUM, AND GETTING NOWHERE FAST

Balance Total Cost Total Time

$1,000 $2,590.35 17 years, 3 months

$2,500 $7,733.49 30 years, 3 months

$5,000 $16,305.34 40 years, 2 months

The cost – in years and dollars -- of paying the minimum 2% of balances on credit cards charging 17% annual interest:

Source: www.bankrate.com

10-19

• Revolving charge account -- allows the buyer open-end credit up to the maximum credit limit.

Fair Credit

and Charge

Card

Disclosur

e Act of

1988.

REVOLVING CHARGE CREDIT CARDS

• Interest charges are based on the interest rate times the previous month’s balance (outstanding balance).

• Payments are first applied towards interest and then the outstanding balance (US Rule).

10-20

SCHEDULE OF PAYMENTS(TABLE 10.1)

Monthly Outstanding Amount of Payment Balance 1 1/2% Interest Monthly Reduction in OutstandingNumber Due Payment Payment Balance Due Balance Due

1 $8,000.00 $120.00 $500 $380.00 $7,620.00

(.015 x $8,000) ($500 - $120) ($8,000 - $380) 2 $7,620.00 $114.30 $500 $385.70 $7,234.30

(.015 x $7,620) ($500 - $114.30) ($7,620 - $385.70) 3 $7,234.30 $108.51 $500 $391.49 $6,842.81

(.015 x $7,234.30) ($500 - $108.51)($7,234.30-$391.49)

10-21

Step 2. When the daily balance is the same for more than one day, multiply it by the number of days the daily balance remained the same or the number of days of the current balance. This gives a cumulative daily balance.

Step 3. Add the cumulative balances.

Step 4. Divide the sum of the cumulative daily balances by the number of days in the billing cycle.

CALCULATING AVERAGE DAILY BALANCE

Step 5. Finance charge = Rate per month x Average daily balance

10-22

Step 1. Calculate the daily balance or amount owed at the end of each day during the billing cycle:

Daily Previous Cash balance balance advances

= + + Purchases -- Payments

30-day billing cycle6/20 Billing date Previous balance $4506/27 Payment $50cr.6/30 Charge: JCPenney 2007/9 Payment 40cr.7/12 Cash advance 60

CALCULATING AVERAGE DAILY BALANCE

Rate 1 ½ % per month on average daily balance.

10-23

Calculate the balance outstanding at the end of month 2 (use U.S. Rule) given the following: purchased $600 desk; pay back $40 per month; and charge of 2 ½% interest on unpaid balance.

Days Current Daily BalanceExtension

7 $450 $3,1503 400 ($450 -- $50) 2,1009 600 ($400 + $200) 5,4003 560 ($600 -- $40) 1,6808 620 ($560 + $60) 4,96030 $16,390

Average daily balance = $16,390 = $546.33

30

Finance charge = $546.33 x .015) = $8.19

CALCULATING AVERAGE DAILY BALANCE

30 - 22

10-24

(7+3+9+3)Step 1

Step 2

Step 3

Step 4

Step 5