McGraw-Hill/Irwin ©2008 The McGraw-Hill Companies, All Rights Reserved

Chapter 14

Installment Buying, Rule Installment Buying, Rule of 78, and Revolving of 78, and Revolving Charge Credit CardsCharge Credit Cards

14-2

• Calculate the amount financed, finance charge, and deferred payment

• Calculate the estimated APR by table lookup

• Calculate the monthly payment by formula and by table lookup

Installment Buying, Rule of 78, and Revolving Charge Credit Cards#14#14Learning Unit ObjectivesCost of Installment BuyingLU14.1LU14.1

14-3

• Calculate the rebate and payoff for Rule of 78

Installment Buying, Rule of 78, and Revolving Charge Credit Cards#14#14Learning Unit ObjectivesPaying Off Installment Loan before Due Date

LU14.2LU14.2

14-4

• Calculate the finance charges on revolving charge credit card accounts

Installment Buying, Rule of 78, and Revolving Charge Credit Cards#14#14Learning Unit ObjectivesRevolving Charge Credit CardsLU14.3LU14.3

14-5

Finance charge (FC) - the interest charge.

FC = Total of all - Amount monthly payments financed

Installment loan - a loan paid of 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

14-6

Cost of Installment Buying

Mary Wilson would like to buy a boat 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

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

Finance Charge = Total of all - Amount monthly payments financed

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

Deferred payment = Total of all + Down Price monthly payment

payments

$11,962.80 = $11,662.80 + $300

14-7

Calculating APR by Table

Step 1. Divide the finance charge by amount financed and multiply by $100 to get the table lookup factor.

Step 2. Go to APR Table 14.1. At the left side of the table are listed the number of payments that will be made.

Step 3. When you find the number of payments you are looking for, move to the right and look for the two numbers closest to the table lookup number. This will indicate the APR.

14-8

Annual Percentage Rate (APR)

Calculating APR rate by table

Finance charge x $100 = Table 14.1Amount financed lookup #

$2,617.80 x 100 = $28.94 $9,045

Between 10.25% - 10.50%

Truth in

Lending Act

APR must be

accurate to

the nearest

1/4 of 1%

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# of Payments 10.00% 10.25% 10.50% 10.75% 11.00% 11.25% 11.50% 11.75% 12.00% 12.25% 12.50%

36 16.16 16.58 17.01 17.43 17.86 18.29 18.71 19.14 19.57 20.00 20.43

37 16.62 17.06 17.49 17.93 18.37 18.81 19.25 19.69 20.13 20.58 21.02

38 17.08 17.53 17.98 18.43 18.88 19.33 19.78 20.24 20.69 21.15 21.61

39 17.54 18.00 18.46 18.93 19.39 19.86 20.32 20.79 21.26 21.73 22.20

40 18.00 18.48 18.95 19.43 19.90 20.38 20.86 21.34 21.82 22.30 22.79

41 18.47 18.95 19.44 19.93 20.42 20.91 21.40 21.89 22.39 22.88 23.38

42 18.93 19.43 19.93 20.43 20.93 21.44 21.94 22.45 22.96 23.47 23.98

43 19.40 19.91 20.42 20.94 21.45 21.97 22.49 23.01 23.53 24.05 24.57

44 19.86 20.39 20.91 21.44 21.97 22.50 23.03 23.57 24.10 24.64 25.17

45 20.33 20.87 21.41 21.95 22.49 23.03 23.58 24.12 24.67 25.22 25.77

46 20.80 21.35 21.90 22.46 23.01 23.57 24.13 24.69 25.25 25.81 26.37

47 21.27 21.83 22.40 22.97 23.53 24.10 24.68 25.25 25.82 26.40 26.98

48 21.74 22.32 22.90 23.48 24.06 24.64 25.23 25.81 26.40 26.99 27.58

49 22.21 22.80 23.39 23.99 24.58 25.18 25.78 26.38 26.98 27.59 28.19

50 22.69 23.29 23.89 24.50 25.11 25.72 26.33 26.95 27.56 28.18 28.80

60 27.48 28.22 28.96 29.71 30.45 31.20 31.96 32.71 33.47 34.23 34.99

Annual percentage rate table per $100 (Partial)

Table 14.1 - Annual Percentage Rate Table per $100

14-10

Calculating the Monthly Payment by Formula

Finance charge + Amount financedNumber of payments of loan

$2,617.80 + $9,04560

$194.38

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Step 2. Look up the rate (10.5%) and the number of months (60). At the intersection is the table factor showing the monthly payment per $1,000 ($21.49)

Step 3. Multiply the quotient in Step 1 by the factor in Step 2

9.045 x $21.49 = $194.38

Calculating the Monthly Payment by Table

Step 1. Divide the loan amount by $1,000

$9,045 = 9.045$1,000

14-12

Table 14.2 - Loan Amortization Table(Monthly payment per $1,000 to pay principal and interest on installment loan)

(Partial)

Terms inmonths 7.50% 8.00% 8.50% 9.00% 10.00% 10.50% 11.00% 11.50% 12.00%

6 $170 $171 $171 $171 $172 $172 $172 $172 $17312 86.76 86.99 87.22 87.46 87.92 88.15 88.38 88.62 88.8518 58.9 59.15 59.37 59.6 60.06 60.29 60.52 60.75 60.9824 45 45.23 45.46 45.69 46.14 46.38 46.61 46.84 47.0730 36.66 36.89 37.12 37.35 37.81 38.04 38.28 38.51 38.7536 31.11 31.34 31.57 31.8 32.27 32.5 32.74 32.98 33.2142 27.15 27.38 27.62 27.85 28.32 28.55 28.79 29.03 29.2848 24.18 24.42 24.65 24.77 25.36 25.6 25.85 26.09 26.3354 21.88 22.12 22.36 22.59 23.07 23.32 23.56 23.81 24.0660 20.04 20.28 20.52 20.76 21.25 21.49 21.74 21.99 22.24

14-13

Calculating Rebate and Payoff for Rule of 78

Rule of 78 - A variation of the U. S. Rule. The Rule of 78 is not allowed for loans of 61 months or longer

Step 1. Find the balance of the loan outstanding

Step 2. Calculate the total finance charge

Step 3. Find the number of payments remaining

Step 4. Set up the rebate fraction from Table 14.3

Step 5. Calculate the rebate amount of the finance charge

Step 6. Calculate the payoff

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Table 14.3 - Rebate Fraction Table based on Rule of 78

Months Sum of Months Sum ofto go digits to go digits

1 1 31 4962 3 32 5283 6 33 5614 10 34 5955 15 35 6306 21 36 6667 28 37 7038 36 38 7419 45 39 780

10 55 40 82011 66 41 86112 78 42 90313 91 43 94614 105 44 99015 120 45 103516 136 46 108117 153 47 112818 171 48 117619 190 49 122520 210 50 127521 231 51 132622 253 52 137823 276 53 143124 300 54 148525 325 55 154026 351 56 159627 378 57 165328 406 58 171129 435 59 177030 465 60 1830 60 Months

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Paying Off Installment Loan before Due Date

What is the rebate of the finance charge and payoff if the car loan were paid off after 27 months?

1. 60 x$ 194.38 = $11,662.80 - 27 x $194.38 = $ 5,248.26 Bal. Out.= $ 6,414.54

2. $11,662.80 - $ 9,045.00 $ 2,617.80 = Total fin. chr.

3. 60 - 27 = 33 Pymts. remaining

4. 561 - Sum of digits 33 mnths 1,830 - Sum of digits 60 mnths

5. 561 x $2,617.80 = $802.51 1,830

6. $6414.54 - $802.51 = $5,612.03

14-16

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

Fair Credit

and Charge

Card

Disclosure

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)

14-17

Paying Just the Minimum, and Get 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

14-18

Table 14.4 - Schedule of Payments

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)

14-19

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 balances.

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

Daily = Previous + Cash + Purchases - Paymentsbalance balance advances

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

14-20

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

14-21

Days Current daily bal. Extension

7 $450 $3,1503 400 ($450- $50) 1,2009 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

Step 1Step 2

Step 3

Step 430-22

Calculating Average Daily Balance

Step 5

(7+3+9+2)

14-22

Problem 14-10:

$35,300 - 3,530 down payment$31,770 loan amount

$31,770 $1,000

= $31.77 x 20.28 = $664.2956 = $644.30

Solution:

14-23

Problem 14-12:

a. Amount financed: $7,880 - 0 =$7,880 Selling Down Amount price payment financed

- =

b. Finance charge: ($185.53 x 60) - $7,880 = $3,251.80

C. APR by table lookup: $3,251.80 X $100 = $41.27

$7,880.00

Between 14.50% and 14.75%

d. Monthly payment by formula: $3,251.80 + $7,880.0 = $185.5360

e. Monthly payment by table lookup (use 14.50%):

$7,880 = 7.88 $23.53 = $185.42

$1,000

Solution:

14-24

Problem 14-17:

First America Bank U.S. Bank

$488.26 x 48 = $23,436.48 $497.70 x 48 = $23,889.60

- 20,000.00 - 20,000.00

$ 3,436.48 finance charge $ 3,889.60 finance charge

$3,436.48 x $100 = $17.1824 $3,889.60 x $100 = $19.448

$20,000 $20,000

= Between 8.00% and 8.25% = Between 8.75% and 9%

Solution:

14-25

Problem 14-18:

No. of days Current

Of current balance Balance Extension

6 $ 800 $4,800

5 740 3,700

7 990 6,930

4 970 3,880

6 (28 – 22) 1,170 7,020

$26,330 ÷ 28 = $940.35714

Solution:

14-26

Problem 14-19:

Monthly 1½ % Amount of Outstanding

Payment Outstanding interest monthly Reduction in Balance due

Number balance due payment payment balance due

1 $500.00 $7.50 $100.00 $92.50 $407.50

($500 x .015) ($100.00 - $7.50) ($500 - $92.50)

2 $407.50 $6.11 $100.00 $93.89 $313.61

($407.50 x .015) ($100.00 - $6.11) ($407.50 - $93.89)

3 $313.61 $4.70 $100.00 $95.30 $218.31 ($313.61 x .015) ($100.00 - $4.70) ($313.61 - $95.30)

Solution: