CHAPTER
12
Consumer Credit
ISBN 1-256-64971-6
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
Get Out of Debt Diet
Having trouble paying your bills? Constantly making minimum payments each month? Don’t know how much you owe?
Worried about getting a bad credit report? According to IndexCreditCards.com, the average U.S. household has credit card
debt of over $7,300, with interest rates ranging from the middle to high teens. Credit card companies have made running
up that balance deceptively easy.
However, there are a number of steps you can take to pay
off the debt and get back on track. Of course, this will require
you to adjust your spending habits and become more careful
about your spending.
1. Determine what you owe. Make a list of all the debts
you have including the name of the creditor, your total
balance, your minimum monthly payment, and your
interest rate. This will help you determine in which order
you should pay down your debts.
2. Pay it down. Work overtime or take on a second job and
devote that income to paying down debt. Cash in CDs, pay
down home equity loans, and pay down loans against retirement. Have a garage sale. Do whatever you can to earn extra
money and devote that money to paying down your debt.
3. Reduce expenses. Eliminate any unnecessary expenses
such as eating out and expensive entertainment. Clip
coupons, shop at sales, and avoid impulse purchases. Brown
bag it at work and be creative about gifts. Above all, stop
using credit cards. Just giving up that expensive cup of coffee
each morning can save you more than $750 dollars a year.
4. Record your spending. This is actually your key to
getting out of debt. You’re in debt because you spent
money you didn’t have. Avoiding more debt starts with
knowing what you are spending your money on. Each day
for at least one month, write down every amount you
spend, no matter how small. Reviewing how you spend
your money allows you to set priorities.
5. Make a budget based on your spending record. Write
down the amount you spent in each category of spending
last month as you budget for spending for the next month.
Categorize your monthly expenses into logical groups
such as necessities (food, rent, medicine, pet food, and so
on), should have (things you need but not immediately,
such as new workout gear), and like to have (things you
don’t need but enjoy (magazines, cable television). One
expense should be paying off your debt. Did you know
that making a minimum payment of $26 on a single credit
card with a $1,000 balance and 19% interest will take
more than five years to pay off?
6. Pay cash. This results in a significant savings in terms of
what you purchase and not having to pay interest on those
purchases. When you don’t have the cash, you don’t buy.
7. Resolve to spend less than you make. Realize once and for
all that if you can’t pay for it today then you can’t afford it.
Managing your credit and knowing exactly how much you
are paying for using credit are important concepts that you
will learn in this chapter.
LEARNING OUTCOMES
12-1 Installment Loans and Closed-End Credit
ISBN 1-256-64971-6
1. Find the amount financed, the installment price, and the finance
charge of an installment loan.
2. Find the installment payment of an installment loan.
3. Find the estimated annual percentage rate (APR) using a table.
12-3 Open-End Credit
1. Find the finance charge and new balance using the average daily
balance method.
2. Find the finance charge and new balance using the unpaid or
previous month’s balance.
12-2 Paying a Loan Before It Is Due: The Rule of 78
1. Find the interest refund using the rule of 78.
Two corresponding Business Math Case Videos for this chapter, Which
Credit Card Deal is Best? and Should I Buy or Lease a Car? can be
found online at www.pearsonhighered.com\cleaves.
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
Consumer credit: a type of credit or loan that
is available to individuals or businesses. The
loan is repaid in regular payments.
Installment loan: a loan that is repaid in
regular payments.
Closed-end credit: a type of installment loan in
which the amount borrowed and the interest
are repaid in a specified number of equal
payments.
Open-end credit: a type of installment loan in
which there is no fixed amount borrowed or
fixed number of payments. Payments are made
until the loan is paid off.
Many individuals and businesses make purchases for which they do not pay the full amount at
the time of purchase. These purchases are paid for by paying a portion of the amount owed in
regular payments until the loan is completely paid. This type of loan or credit is often referred to
as consumer credit.
In the preceding chapters we discussed the interest to be paid on loans that are paid in full on
the date of maturity of the loan. Many times, loans are made so that the maker (the borrower) pays
a given amount in regular payments. Loans with regular payments are called installment loans.
There are two kinds of installment loans. Closed-end credit is a type of loan in which the
amount borrowed plus interest is repaid in a specified number of equal payments. Examples include bank loans and loans for large purchases such as cars and appliances. Open-end credit is
a type of loan in which there is no fixed number of payments—the person keeps making payments until the amount is paid off, and the interest is computed on the unpaid balance at the end
of each payment period. Credit card accounts, retail store accounts, and line-of-credit accounts
are types of open-end credit.
12-1 INSTALLMENT LOANS AND CLOSED-END CREDIT
LEARNING OUTCOMES
1 Find the amount financed, the installment price, and the finance charge of an
installment loan.
2 Find the installment payment of an installment loan.
3 Find the estimated annual percentage rate (APR) using a table.
Finance charges or carrying charges: the
interest and any fee associated with an
installment loan.
Should you or your business take out an installment loan? That depends on the interest you will
pay and how it is computed. The interest associated with an installment loan is part of the
charges referred to as finance charges or carrying charges. In addition to accrued interest
charges, installment loans often include charges for insurance, credit-report fees, or loan fees.
Under the truth-in-lending law, all of these charges must be disclosed in writing to the consumer.
1 Find the amount financed, the installment price,
and the finance charge of an installment loan.
Cash price: the price if all charges are paid at
once at the time of the purchase.
Down payment: a partial payment that is paid
at the time of the purchase.
Amount financed: the cash price minus the
down payment.
The cash price is the price you pay if you pay all at once at the time of the purchase. If you pay
on an installment basis instead, the down payment is a partial payment of the cash price at the
time of the purchase. The amount financed is the cash price minus the down payment. The
installment payment is the amount you pay each period, including interest, to pay off the loan.
The installment price is the total paid, including all of the installment payments, the finance
charges, and the down payment.
Installment payment: the amount that is paid
(including interest) in each regular payment.
Installment price: the total amount paid for a
purchase, including all payments, the finance
charges, and the down payment.
Find the amount financed and the installment price
HOW TO
1. Find the amount financed: Subtract the down payment from the cash price.
Amount financed = cash price - down payment
2. Find the installment price: Add the down payment to the total of the installment payments.
Installment price = total of installment payments + down payment
EXAMPLE 1
The 7th Inning purchased a mat cutter for the framing department
on the installment plan with a $600 down payment and 12 payments of $145.58. Find the installment price of the mat cutter.
426
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
Total of
number of
installment
installment = a
b * a
b
installments
payment
payments
=
12
*
$145.58
= $1,746.96
Installment price = total of installment payments + down payment
= $1,746.96 + $600
= $2,346.96
The installment price is $2,346.96.
Find the finance charge of an installment loan
HOW TO
1. Determine the cash price of the item.
2. Find the installment price of the item.
3. Subtract the result found in step 2 from the result of step 1.
Finance charge installment price cash price
EXAMPLE 2
If the cash price of the mat cutter in Example 1 was $2,200, find
the finance charge and the amount financed.
Finance charge = installment price - cash price Installment price = $2,346.96
= $2,346.96 - $2,200.00
Cash price = $2,200.00
= $146.96
Down payment = $600
Amount financed = cash price - down payment.
= $2,200 - $600
= $1,600
The finance charge is $146.96 and the amount financed is $1,600.
STOP AND CHECK
1. An ice machine with a cash price of $1,095 is purchased
on the installment plan with a $100 down payment and
18 monthly payments of $62.50. Find the amount financed,
installment price, and finance charge for the machine.
2. A copy machine is purchased on the installment plan with a
$200 down payment and 24 monthly payments of $118.50.
The cash price is $2,695. Find the amount financed,
installment price, and finance charge for the machine.
3. An industrial freezer with a cash price of $2,295 is
purchased on the installment plan with a $275 down
payment and 30 monthly installment payments of $78.98.
Find the amount financed, installment price, and finance
charge for the freezer.
4. The cash price of a music system is $2,859 and the
installment price is $3,115.35. How much is the finance
charge?
2
Find the installment payment of an installment loan.
Since the installment price is the total of the installment payments plus the down payment, we
can find the installment payment if we know the installment price, the down payment, and the
number of payments.
HOW TO
Find the installment payment, given the installment price, the down
payment, and the number of payments
ISBN 1-256-64971-6
1. Find the total of the installment payments: Subtract the down payment from the installment price.
Total of installment payments = installment price - down payment
2. Divide the total of the installment payments by the number of installment payments.
Installment payment =
total of installment payments
number of payments
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
427
TIP
Protect Your Credit Rating
Your credit reputation is just as
important as your personal reputation. Three different agencies track
credit records. They are Equifax,
Experian, and TransUnion. You
are entitled to a free annual credit
report from each of these three
nationwide consumer reporting
agencies.
E X A M P L E 3 The installment price of a drafting table was $1,627 for a 12-month
loan. If a $175 down payment had been made, find the installment payment.
Total of installment payments = installment price - down payment
= $1,627 - $175 = $1,452
total of installment payments
Installment payment =
number of payments
$1,452
=
= $121
12
Subtract.
Divide.
The installment payment is $121.
STOP AND CHECK
1. The installment price of a refrigerator is $2,087 for a
24-month loan. If a down payment of $150 had been made,
what is the installment payment?
2. The installment price of a piano is $8,997.40 and a down
payment of $1,000 is made. What is the monthly
installment payment if the piano is financed for 36 months?
3. The installment price of a tire machine is $2,795.28. A
down payment of $600 is made. What is the installment
payment if the machine is financed for 36 months?
4. Find the installment payment for a trailer if its installment
price is $3,296.96 over 30 months and an $800 down
payment is made.
3 Find the estimated annual percentage rate (APR) using a table.
Annual percentage rate (APR): the equivalent
rate of an installment loan that is equivalent to
an annual simple interest rate.
In 1969 the federal government passed the Consumer Credit Protection Act, Regulation Z, also
known as the Truth-in-Lending Act. Several amendments have been made to this original legislation. It requires that a lending institution tell the borrower, in writing, what the actual annual
rate of interest is as it applies to the balance due on the loan each period. This interest rate tells
the borrower the true cost of the loan.
If you borrowed $1,500 for a year and paid an interest charge of $165, you would be paying
an interest rate of 11% annually on the entire $1,500 (165 , $1,500 = 0.11 = 11%). But if
you paid the money back in 12 monthly installments of $138.75 ([$1,500 + $165] , 12 =
$138.75), you would not have the use of the $1,500 for a full year. Instead, you would be paying
it back in 12 payments of $138.75 each. Thus, you are losing the use of some of the money every
month but are still paying interest at the rate of 11% of the entire amount. This means that you
are actually paying more than 11% interest. The equivalent rate is the annual percentage rate
(APR). Applied to installment loans, the APR is the annual simple interest rate equivalent that is
actually being paid on the unpaid balances. The APR can be determined using a government-issued table.
The federal government issues annual percentage rate tables, which are used to find APR
rates (within 14%, which is the federal standard). A portion of one of these tables, based on the
number of monthly payments, is shown in Table 12-1.
HOW TO
Find the estimated annual percentage rate using a per $100
of amount financed table
1. Find the interest per $100 of amount financed: Divide the finance charge including interest
by the amount financed and multiply by $100.
finance charge
* $100
amount financed
2. Find the row corresponding to the number of monthly payments. Move across the row to
find the number closest to the value from step 1. Read up the column to find the annual
percentage rate for that column. If the result in step 1 is exactly halfway between two table
values, a rate halfway between the two rates can be used.
428
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
Interest per $100 =
TABLE 12-1
ISBN 1-256-64971-6
Interest per $100 of Amount Financed
Number
of monthly
payments
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
APR (Annual Percentage Rate) for Selected Rates
10.75%
0.90
1.35
1.80
2.25
2.70
3.16
3.62
4.07
4.53
4.99
5.45
5.92
6.38
6.85
7.32
7.78
8.25
8.73
9.20
9.67
10.15
10.62
11.10
11.58
12.06
12.54
13.03
13.51
14.00
14.48
14.97
15.46
15.95
16.44
16.94
17.43
17.93
18.43
18.93
19.43
19.93
20.43
20.94
21.44
21.95
22.46
22.97
23.48
23.99
24.50
25.02
25.53
26.05
26.57
27.09
27.61
28.13
28.66
29.18
29.71
11.00% 11.25% 11.50% 11.75% 12.00% 12.25% 12.50% 12.75% 13.00% 13.25% 13.50% 13.75% 14.00% 14.25% 15.00%
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.15
1.17
1.19
1.25
1.38
1.41
1.44
1.47
1.50
1.53
1.57
1.60
1.63
1.66
1.69
1.72
1.75
1.78
1.88
1.84
1.88
1.92
1.96
2.01
2.05
2.09
2.13
2.17
2.22
2.26
2.30
2.34
2.38
2.51
2.30
2.35
2.41
2.46
2.51
2.57
2.62
2.67
2.72
2.78
2.83
2.88
2.93
2.99
3.14
2.77
2.83
2.89
2.96
3.02
3.08
3.15
3.21
3.27
3.34
3.40
3.46
3.53
3.59
3.78
3.23
3.31
3.38
3.45
3.53
3.60
3.68
3.75
3.83
3.90
3.97
4.05
4.12
4.20
4.42
3.70
3.78
3.87
3.95
4.04
4.12
4.21
4.29
4.38
4.47
4.55
4.64
4.72
4.81
5.06
4.17
4.26
4.36
4.46
4.55
4.65
4.74
4.84
4.94
5.03
5.13
5.22
5.32
5.42
5.71
4.64
4.75
4.85
4.96
5.07
5.17
5.28
5.39
5.49
5.60
5.71
5.82
5.92
6.03
6.35
5.11
5.23
5.35
5.46
5.58
5.70
5.82
5.94
6.05
6.17
6.29
6.41
6.53
6.65
7.00
5.58
5.71
5.84
5.97
6.10
6.23
6.36
6.49
6.62
6.75
6.88
7.01
7.14
7.27
7.66
6.06
6.20
6.34
6.48
6.62
6.76
6.90
7.04
7.18
7.32
7.46
7.60
7.74
7.89
8.31
6.53
6.68
6.84
6.99
7.14
7.29
7.44
7.59
7.75
7.90
8.05
8.20
8.36
8.51
8.97
7.01
7.17
7.34
7.50
7.66
7.82
7.99
8.15
8.31
8.48
8.64
8.81
8.97
9.13
9.63
7.49
7.66
7.84
8.01
8.19
8.36
8.53
8.71
8.88
9.06
9.23
9.41
9.59
9.76
10.29
7.97
8.15
8.34
8.53
8.71
8.90
9.08
9.27
9.46
9.64
9.83
10.02
10.20
10.39
10.95
8.45
8.65
8.84
9.04
9.24
9.44
9.63
9.83
10.03
10.23
10.43
10.63
10.82
11.02
11.62
8.93
9.14
9.35
9.56
9.77
9.98
10.19
10.40
10.61
10.82
11.03
11.24
11.45
11.66
12.29
9.42
9.64
9.86
10.08
10.30
10.52
10.74
10.96
11.18
11.41
11.63
11.85
12.07
12.30
12.97
9.90
10.13
10.37
10.60
10.83
11.06
11.30
11.53
11.76
12.00
12.23
12.46
12.70
12.93
13.64
10.39
10.63
10.88
11.12
11.36
11.61
11.85
12.10
12.34
12.59
12.84
13.08
13.33
13.58
14.32
10.88
11.13
11.39
11.64
11.90
12.16
12.41
12.67
12.93
13.19
13.44
13.70
13.96
14.22
15.00
11.37
11.63
11.90
12.17
12.44
12.71
12.97
13.24
13.51
13.78
14.05
14.32
14.59
14.87
15.68
11.86
12.14
12.42
12.70
12.98
13.26
13.54
13.82
14.10
14.38
14.66
14.95
15.23
15.51
16.37
12.35
12.64
12.93
13.22
13.52
13.81
14.10
14.40
14.69
14.98
15.28
15.57
15.87
16.17
17.06
12.85
13.15
13.45
13.75
14.06
14.36
14.67
14.97
15.28
15.59
15.89
16.20
16.51
16.82
17.75
13.34
13.66
13.97
14.29
14.60
14.92
15.24
15.56
15.87
16.19
16.51
16.83
17.15
17.47
18.44
13.84
14.16
14.49
14.82
15.15
15.48
15.81
16.14
16.47
16.80
17.13
17.46
17.80
18.13
19.14
14.33
14.67
15.01
15.35
15.70
16.04
16.38
16.72
17.07
17.41
17.75
18.10
18.45
18.79
19.83
14.83
15.19
15.54
15.89
16.24
16.60
16.95
17.31
17.66
18.02
18.38
18.74
19.10
19.45
20.54
15.33
15.70
16.06
16.43
16.79
17.16
17.53
17.90
18.27
18.63
19.00
19.38
19.75
20.12
21.24
15.84
16.21
16.59
16.97
17.35
17.73
18.11
18.49
18.87
19.25
19.63
20.02
20.40
20.79
21.95
16.34
16.73
17.12
17.51
17.90
18.29
18.69
19.08
19.47
19.87
20.26
20.66
21.06
21.46
22.65
16.85
17.25
17.65
18.05
18.46
18.86
19.27
19.67
20.08
20.49
20.90
21.31
21.72
22.13
23.37
17.35
17.77
18.18
18.60
19.01
19.43
19.85
20.27
20.69
21.11
21.53
21.95
22.38
22.80
24.08
17.86
18.29
18.71
19.14
19.57
20.00
20.43
20.87
21.30
21.73
22.17
22.60
23.04
23.48
24.80
18.37
18.81
19.25
19.69
20.13
20.58
21.02
21.46
21.91
22.36
22.81
23.25
23.70
24.16
25.51
18.88
19.33
19.78
20.24
20.69
21.15
21.61
22.07
22.52
22.99
23.45
23.91
24.37
24.84
26.24
19.39
19.86
20.32
20.79
21.26
21.73
22.20
22.67
23.14
23.61
24.09
24.56
25.04
25.52
26.96
19.90
20.38
20.86
21.34
21.82
22.30
22.79
23.27
23.76
24.25
24.73
25.22
25.71
26.20
27.69
20.42
20.91
21.40
21.89
22.39
22.88
23.38
23.88
24.38
24.88
25.38
25.88
26.39
26.89
28.41
20.93
21.44
21.94
22.45
22.96
23.47
23.98
24.49
25.00
25.51
26.03
26.55
27.06
27.58
29.15
21.45
21.97
22.49
23.01
23.53
24.05
24.57
25.10
25.62
26.15
26.68
27.21
27.74
28.27
29.88
21.97
22.50
23.03
23.57
24.10
24.64
25.17
25.71
26.25
26.79
27.33
27.88
28.42
28.97
30.62
22.49
23.03
23.58
24.12
24.67
25.22
25.77
26.32
26.88
27.43
27.99
28.55
29.11
29.67
31.36
23.01
23.57
24.13
24.69
25.25
25.81
26.37
26.94
27.51
28.08
28.65
29.22
29.79
30.36
32.10
23.53
24.10
24.68
25.25
25.82
26.40
26.98
27.56
28.14
28.72
29.31
29.89
30.48
31.07
32.84
24.06
24.64
25.23
25.81
26.40
26.99
27.58
28.18
28.77
29.37
29.97
30.57
31.17
31.77
33.59
24.58
25.18
25.78
26.38
26.98
27.59
28.19
28.80
29.41
30.02
30.63
31.24
31.86
32.48
34.34
25.11
25.72
26.33
26.95
27.56
28.18
28.80
29.42
30.04
30.67
31.29
31.92
32.55
33.18
35.09
25.64
26.26
26.89
27.52
28.15
28.78
29.41
30.05
30.68
31.32
31.96
32.60
33.25
33.89
35.84
26.17
26.81
27.45
28.09
28.73
29.38
30.02
30.67
31.32
31.98
32.63
33.29
33.95
34.61
36.60
26.70
27.35
28.00
28.66
29.32
29.98
30.64
31.30
31.97
32.63
33.30
33.97
34.65
35.32
37.36
27.23
27.90
28.56
29.23
29.91
30.58
31.25
31.93
32.61
33.29
33.98
34.66
35.35
36.04
38.12
27.77
28.44
29.13
29.81
30.50
31.18
31.87
32.56
33.26
33.95
34.65
35.35
36.05
36.76
38.88
28.30
28.99
29.69
30.39
31.09
31.79
32.49
33.20
33.91
34.62
35.33
36.04
36.76
37.48
39.65
28.84
29.54
30.25
30.97
31.68
32.39
33.11
33.83
34.56
35.28
36.01
36.74
37.47
38.20
40.42
29.37
30.10
30.82
31.55
32.27
33.00
33.74
34.47
35.21
35.95
36.69
37.43
38.18
38.93
41.19
29.91
30.65
31.39
32.13
32.87
33.61
34.36
35.11
35.86
36.62
37.37
38.13
38.89
39.66
41.96
30.45
31.20
31.96
32.71
33.47
34.23
34.99
35.75
36.52
37.29
38.06
38.83
39.61
40.39
42.74
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
429
TABLE 12-1
Interest per $100 of Amount Financed—Continued
430
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
Number
APR (Annual Percentage Rate) for Selected Rates
of monthly
payments 15.50% 15.75% 16.00% 16.25% 16.50% 16.75% 17.00% 19.50% 19.75% 20.00% 20.25% 20.50% 20.75% 21.00% 21.25% 21.50%
1
1.29
1.31
1.33
1.35
1.37
1.40
1.42
1.62
1.65
1.67
1.69
1.71
1.73
1.75
1.77
1.79
2
1.94
1.97
2.00
2.04
2.07
2.10
2.13
2.44
2.48
2.51
2.54
2.57
2.60
2.63
2.66
2.70
3
2.59
2.64
2.68
2.72
2.76
2.80
2.85
3.27
3.31
3.35
3.39
3.44
3.48
3.52
3.56
3.60
4
3.25
3.30
3.36
3.41
3.46
3.51
3.57
4.10
4.15
4.20
4.25
4.31
4.36
4.41
4.47
4.52
5
3.91
3.97
4.04
4.10
4.16
4.23
4.29
4.93
4.99
5.06
5.12
5.18
5.25
5.31
5.37
5.44
6
4.57
4.64
4.72
4.79
4.87
4.94
5.02
5.76
5.84
5.91
5.99
6.06
6.14
6.21
6.29
6.36
7
5.23
5.32
5.40
5.49
5.58
5.66
5.75
6.60
6.69
6.78
6.86
6.95
7.04
7.12
7.21
7.29
8
5.90
6.00
6.09
6.19
6.29
6.38
6.48
7.45
7.55
7.64
7.74
7.84
7.94
8.03
8.13
8.23
9
6.57
6.68
6.78
6.89
7.00
7.11
7.22
8.30
8.41
8.52
8.63
8.73
8.84
8.95
9.06
9.17
10
7.24
7.36
7.48
7.60
7.72
7.84
7.96
9.15
9.27
9.39
9.51
9.63
9.75
9.88
10.00
10.12
11
7.92
8.05
8.18
8.31
8.44
8.57
8.70
10.01
10.14
10.28
10.41
10.54
10.67
10.80
10.94
11.07
12
8.59
8.74
8.88
9.02
9.16
9.30
9.45
10.87
11.02
11.16
11.31
11.45
11.59
11.74
11.88
12.02
13
9.27
9.43
9.58
9.73
9.89
10.04
10.20
11.74
11.90
12.05
12.21
12.36
12.52
12.67
12.83
12.99
14
9.96
10.12
10.29
10.45
10.67
10.78
10.95
12.61
12.78
12.95
13.11
13.28
13.45
13.62
13.79
13.95
15
10.64
10.82
11.00
11.17
11.35
11.53
11.71
13.49
13.67
13.85
14.03
14.21
14.39
14.57
14.75
14.93
16
11.33
11.52
11.71
11.90
12.09
12.28
12.46
14.37
14.56
14.75
14.94
15.13
15.33
15.52
15.71
15.90
17
12.02
12.22
12.42
12.62
12.83
13.03
13.23
15.25
15.46
15.66
15.86
16.07
16.27
16.48
16.68
16.89
18
12.72
12.93
13.14
13.35
13.57
13.78
13.99
16.14
16.36
16.57
16.79
17.01
17.22
17.44
17.66
17.88
19
13.41
13.64
13.86
14.09
14.31
14.54
14.76
17.03
17.26
17.49
17.72
17.95
18.18
18.41
18.64
18.87
20
14.11
14.35
14.59
14.82
15.06
15.30
15.54
17.93
18.17
18.41
18.66
18.90
19.14
19.38
19.63
19.87
21
14.82
15.06
15.31
15.56
15.81
16.06
16.31
18.83
19.09
19.34
19.60
19.85
20.11
20.36
20.62
20.87
22
15.52
15.78
16.04
16.30
16.57
16.83
17.09
19.74
20.01
20.27
20.54
20.81
21.08
21.34
21.61
21.88
23
16.23
16.50
16.78
17.05
17.32
17.60
17.88
20.65
20.93
21.21
21.49
21.77
22.05
22.33
22.61
22.90
24
16.94
17.22
17.51
17.80
18.09
18.37
18.66
21.56
21.86
22.15
22.44
22.74
23.03
23.33
23.62
23.92
25
17.65
17.95
18.25
18.55
18.85
19.15
19.45
22.48
22.79
23.10
23.40
23.71
24.02
24.32
24.63
24.94
26
18.37
18.68
18.99
19.30
19.62
19.93
20.24
23.41
23.73
24.04
24.36
24.68
25.01
25.33
25.65
25.97
27
19.09
19.41
19.74
20.06
20.39
20.71
21.04
24.33
24.67
25.00
25.33
25.67
26.00
26.34
26.67
27.01
28
19.81
20.15
20.48
20.82
21.16
21.50
21.84
25.27
25.61
25.96
26.30
26.65
27.00
27.35
27.70
28.05
29
20.53
20.88
21.23
21.58
21.94
22.29
22.64
26.20
26.56
26.92
27.28
27.64
28.00
28.37
28.73
29.09
30
21.26
21.62
21.99
22.35
22.72
23.08
23.45
27.14
27.52
27.89
28.26
28.64
29.01
29.39
29.77
30.14
31
21.99
22.37
22.74
23.12
23.50
23.88
24.26
28.09
28.47
28.86
29.25
29.64
30.03
30.42
30.81
31.20
32
22.72
23.11
23.50
23.89
24.28
24.68
25.07
29.04
29.44
29.84
30.24
30.64
31.05
31.45
31.85
32.26
33
23.46
23.86
24.26
24.67
25.07
25.48
25.88
29.99
30.40
30.82
31.23
31.65
32.07
32.49
32.91
33.33
34
24.19
24.61
25.03
25.44
25.86
26.28
26.70
30.95
31.37
31.80
32.23
32.67
33.10
33.53
33.96
34.40
35
24.94
25.36
25.79
26.23
26.66
27.09
27.52
31.91
32.35
32.79
33.24
33.68
34.13
34.58
35.03
35.47
36
25.68
26.12
26.57
27.01
27.46
27.90
28.35
32.87
33.33
33.79
34.25
34.71
35.17
35.63
36.09
36.56
37
26.42
26.88
27.34
27.80
28.26
28.72
29.18
33.84
34.32
34.79
35.26
35.74
36.21
36.69
37.16
37.64
38
27.17
27.64
28.11
28.59
29.06
29.53
30.01
34.82
35.30
35.79
36.28
36.77
37.26
37.75
38.24
38.73
39
27.92
28.41
28.89
29.38
29.87
30.36
30.85
35.80
36.30
36.80
37.30
37.81
38.31
38.82
39.32
39.83
40
28.68
29.18
29.68
30.18
30.68
31.18
31.68
36.78
37.29
37.81
38.33
38.85
39.37
39.89
40.41
40.93
41
29.44
29.95
30.46
30.97
31.49
32.01
32.52
37.77
38.30
38.83
39.36
39.89
40.43
40.96
41.50
42.04
42
30.19
30.72
31.25
31.78
32.31
32.84
33.37
38.76
39.30
39.85
40.40
40.95
41.50
42.05
42.60
43.15
43
30.96
31.50
32.04
32.58
33.13
33.67
34.22
39.75
40.31
40.87
41.44
42.00
42.57
43.13
43.70
44.27
44
31.72
32.28
32.83
33.39
33.95
34.51
35.07
40.75
41.33
41.90
42.48
43.06
43.64
44.22
44.81
45.39
45
32.49
33.06
33.63
34.20
34.77
35.35
35.92
41.75
42.35
42.94
43.53
44.13
44.72
45.32
45.92
46.52
46
33.26
33.84
34.43
35.01
35.60
36.19
36.78
42.76
43.37
43.98
44.58
45.20
45.81
46.42
47.03
47.65
47
34.03
34.63
35.23
35.83
36.43
37.04
37.64
43.77
44.40
45.02
45.64
46.27
46.90
47.53
48.16
48.79
48
34.81
35.42
36.03
36.65
37.27
37.88
38.50
44.79
45.43
46.07
46.71
47.35
47.99
48.64
49.28
49.93
49
35.59
36.21
36.84
37.47
38.10
38.74
39.37
45.81
46.46
47.12
47.77
48.43
49.09
49.75
50.41
51.08
50
36.37
37.01
37.65
38.30
38.94
39.59
40.24
46.83
47.50
48.17
48.84
49.52
50.19
50.87
51.55
52.23
51
37.15
37.81
38.46
39.12
39.79
40.45
41.11
47.86
48.55
49.23
49.92
50.61
51.30
51.99
52.69
53.38
52
37.94
38.61
39.28
39.96
40.63
41.31
41.99
48.89
49.59
50.30
51.00
51.71
52.41
53.12
53.83
54.55
53
38.72
39.41
40.10
40.79
41.48
42.17
42.87
49.93
50.65
51.37
52.09
52.81
53.53
54.26
54.98
55.71
54
39.52
40.22
40.92
41.63
42.33
43.04
43.75
50.97
51.70
52.44
53.17
53.91
54.65
55.39
56.14
56.88
55
40.31
41.03
41.74
42.47
43.19
43.91
44.64
52.02
52.76
53.52
54.27
55.02
55.78
56.54
57.30
58.06
56
41.11
41.84
42.57
43.31
44.05
44.79
45.53
53.06
53.83
54.60
55.37
56.14
56.91
57.68
58.46
59.24
57
41.91
42.65
43.40
44.15
44.91
45.66
46.42
54.12
54.90
55.68
56.47
57.25
58.04
58.84
59.63
60.43
58
42.71
43.47
44.23
45.00
45.77
46.54
47.32
55.17
55.97
56.77
57.57
58.38
59.18
59.99
60.80
61.62
59
43.51
44.29
45.07
45.85
46.64
47.42
48.21
56.23
57.05
57.87
58.68
59.51
60.33
61.15
61.98
62.81
60
44.32
45.11
45.91
46.71
47.51
48.31
49.12
57.30
58.13
58.96
59.80
60.64
61.48
62.32
63.17
64.01
E X A M P L E 4 Lewis Strang bought a motorcycle for $3,500, which was financed
at $142 per month for 24 months. The down payment was $500. Find the APR.
Installment price = 24($142) + $500 = $3,408 + $500 = $3,908
Finance charge = $3,908 - $3,500 = $408
Amount financed = $3,500 - $500 = $3,000
finance charge
$408
* $100 =
($100) = $13.60
Interest per $100 =
amount financed
$3,000
Find the row for 24 monthly payments. Move across to find the number nearest to $13.60.
$13.60
- $13.54
$ 0.06
Closest
value
$13.82
- 13.60
$ 0.22
Find the table value closest to $13.60.
Move up to the top of that column to find the annual percentage rate, which is 12.5%.
TIP
Finding the Closest Table Value
Another way to find the closest table value to the interest per $100 is to compare the interest to
the amount halfway between two table values. The halfway amount is the average of the two
table values.
D I D YO U
KNOW?
Not All Quoted APRs Are the Same!
The APR quoted on a loan may or
may not include other fees and charges
associated with a loan such as private
mortgage insurance, processing fees,
and discount points. Some do, some
don’t. Look closely at the details.
Halfway =
larger value + smaller value
2
In the previous example, $13.60 is between $13.54 and $13.82.
$27.36
$13.54 + $13.82
=
2
2
= $13.68
Halfway =
Because $13.60 is less than the halfway amount ($13.68), it is closer to the lower table value
($13.54).
STOP AND CHECK
1. Jaime Lopez purchased a preowned car that listed for
$11,935. After making a down payment of $1,500, he
financed the balance over 36 months with payments of
$347.49 per month. Use Table 12-1 to find the annual
percentage rate (APR) of the loan.
2. Peggy Portzen purchased new kitchen appliances with a
cash price of $6,800. After making a down payment of
$900, she financed the balance over 24 months with
payments of $279.65. Find the annual percentage rate
(APR) of the loan.
3. Alan Dan could purchase a jet ski for $9,995 cash. He paid
$2,000 down and financed the balance with 36 monthly
payments of $295.34. Find the APR of the loan.
4. Nellie Chapman bought a Harley-Davidson motorcycle that
had a cash price of $12,799 with a $2,500 down payment.
She paid for the motorcycle in 48 monthly payments of
$296.37. Find the APR for the loan.
ISBN 1-256-64971-6
12-1 SECTION EXERCISES
SKILL BUILDERS
1. Find the installment price of a recliner bought on the
installment plan with a down payment of $100 and six
payments of $108.20.
2. Find the amount financed if a $125 down payment is made
on a TV with a cash price of $579.
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
431
3. Stephen Helba purchased a TV with surround sound and
remote control on an installment plan with $100 down and
12 payments of $106.32. Find the installment price of the TV.
4. A queen-size bedroom suite can be purchased on an
installment plan with 18 payments of $97.42 if an $80 down
payment is made. What is the installment price of the suite?
5. Zack’s Trailer Sales will finance a 16-foot utility trailer
with ramps and electric brakes. If a down payment of $100
and eight monthly payments of $82.56 are required, what is
the installment price of the trailer?
6. A forklift is purchased for $10,000. The forklift is used as
collateral and no down payment is required. Twenty-four
monthly payments of $503 are required to repay the loan.
What is the installment price of the forklift?
7. A computer with software costs $2,987, and Docie Johnson
has agreed to pay a 19% per year finance charge on the
cash price. If she contracts to pay the loan in 18 months,
how much will she pay each month?
8. The cash price of a bedroom suite is $2,590. There is a 24%
finance charge on the cash price and 12 monthly payments.
Find the monthly payment.
9. Find the monthly payment on a HD LED television with an
installment price of $929, 12 monthly payments, and a
down payment of $100.
10. The installment price of a teakwood extension table and
four chairs is $625 with 18 monthly payments and a down
payment of $75. What is the monthly payment?
APPLICATIONS
11. An entertainment center is financed at a total cost of $2,357
including a down payment of $250. If the center is financed
over 24 months, find the monthly payment.
12. A Hepplewhite sofa costs $3,780 in cash. Jaquanna Wilson
will purchase the sofa in 36 monthly installment payments.
A 13% per year finance charge will be assessed on the
amount financed. Find the finance charge, the installment
price, and the monthly payment.
13. A fishing boat is purchased for $5,600 and financed for
36 months. If the total finance charge is $1,025, find the
annual percentage rate using Table 12-1.
14. An air compressor costs $780 and is financed with monthly
payments for 12 months. The total finance charge is $90.
Find the annual percentage rate using Table 12-1.
15. Jim Meriweather purchased an engraving machine for
$28,000 and financed it for 36 months. The total finance
charge was $5,036. Use Table 12-1 to find the annual
percentage rate.
12-2 PAYING A LOAN BEFORE IT IS DUE: THE RULE OF 78
1 Find the interest refund using the rule of 78.
If a closed-end installment loan is paid entirely before the last payment is actually due, is part of
the interest refundable? In most cases it is, but not always at the rate you might hope. If you paid
a 12-month loan in 6 months, you might expect a refund of half the total interest. However, this
432
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
LEARNING OUTCOME
Rule of 78: method for determining the
amount of refund of the finance charge for an
installment loan that is paid before it is due.
is not the case because the portion of the monthly payment that is interest is not the same from
month to month. In some cases, interest or finance charge refunds are made according to the rule
of 78. Some states allow this method to be used for short-term loans, generally 60 months or less.
Laws and court rulings protect and inform the consumer in matters involving interest.
1
Refund fraction: the fractional part of the total
interest that is refunded when a loan is paid
early using the rule of 78.
Find the interest refund using the rule of 78.
The rule of 78 is not based on the actual unpaid balance after a payment is made. Instead, it is an
approximation that assumes the amount financed (which includes the interest) of a one-year loan
is paid in 12 equal parts. For the first payment, the interest is based on the total amount financed, or
12
11
1
12 of the loan. The interest for the second payment is based on 12 of the amount financed because 12
10
of this amount has already been paid. The interest for the third payment is 12 of the amount
1
financed, and so on. The interest on the last payment is based on 12
of the amount financed.
The sum of all the parts accruing interest for a 12-month loan is 12 + 11 + 10 + 9 + 8 +
7 + 6 + 5 + 4 + 3 + 2 + 1, or 78.
Thus, 78 equal parts accrue interest. The interest each part accrues is the same because the
1
rate is the same and the parts are the same (each is 12
of the principal). Because 78 equal parts
1
each accrue equal interest, the interest each part accrues must be 78
of the total interest for the
one-year loan. So if the loan is paid in full with three months remaining, then the interest that
would have accrued in the 10th, 11th, and 12th months is refunded. In the 10th month, three parts
1
1
each accrue 78
of the total interest; in the 11th month, two parts each accrue 78
of the total inter1
est; and in the 12th month, one part accrues 78 of the total interest. So each of the 3 + 2 + 1
1
6
parts, or 6 parts, accrues 78
of the total interest. Thus 78
of the total interest is refunded. The frac6
tion 78 is called the refund fraction.
Not all installment loans are for 12 months, but the rule of 78 gives us a pattern that we can
apply to loans of any allowable length.
HOW TO
Find the refund fraction for the interest refund
1. The numerator is the sum of the digits from 1 through the number of months remaining of a
loan paid off before it was due.
2. The denominator is the sum of the digits from 1 through the original number of months of
the loan.
3. The original fraction, the reduced fraction, or the decimal equivalent of the fraction can be used.
The sum-of-digits table in Table 12-2 can be used to find the numerator and denominator of
the refund fraction.
TABLE 12-2
ISBN 1-256-64971-6
Sum-of-Digits
Months
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Sum of digits
1
3
6
10
15
21
28
36
45
55
66
78
91
105
120
136
153
171
190
210
Months
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Sum of digits
231
253
276
300
325
351
378
406
435
465
496
528
561
595
630
666
703
741
780
820
Months
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Sum of digits
861
903
946
990
1,035
1,081
1,128
1,176
1,225
1,275
1,326
1,378
1,431
1,485
1,540
1,596
1,653
1,711
1,770
1,830
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
433
There is a shortcut for finding the sum of consecutive numbers beginning with 1. You may
be interested to know that a young boy in elementary school discovered this shortcut in the late
18th century. He later went on to be one of the greatest mathematicians of all time. His name was
Carl Friedrich Gauss (1777–1855).
TIP
The Sum of Consecutive Numbers Beginning with 1
Multiply the largest number by 1 more than the largest number and divide the product by 2.
largest number * (largest number + 1)
2
4(5)
20
Sum of consecutive numbers from 1 through 4 =
=
= 10
2
2
12(13)
156
=
= 78
Sum of consecutive numbers from 1 through 12 =
2
2
Sum of consecutive numbers beginning with 1 =
Find the interest refund using the rule of 78
HOW TO
1. Find the refund fraction.
2. Multiply the total interest by the refund fraction.
Interest refund = total interest * refund fraction
EXAMPLE 1
A loan for 12 months with interest of $117 is paid in full with four
payments remaining. Find the refund fraction for the interest refund.
sum of the digits for number of payments remaining
sum of the digits for total number of payments
1 + 2 + 3 + 4
=
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12
5
10
=
or 0.1282051282
=
10 , 78 = 0.1282051282
78
39
Refund fraction =
10
5
The refund fraction is 78
or 39
or 0.1282051282.
EXAMPLE 2
Find the interest refund for the installment loan in Example 1.
Interest refund = total interest * refund fraction Total interest = $117
10
5
Refund fraction =
or
or 0.1282051282
78 39
Multiply.
= $117(0.1282051282)
= $15
The interest refund is $15.
TIP
CLEAR 117 * 10 , 78 = Q 15
When using a calculator, there is no need to reduce fractions first.
434
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
Continuous Sequence of Steps Using a Calculator
It is advisable in making calculations as in Example 2 that you use a continuous sequence of
steps in a calculator. It is time-consuming and more mistakes are made if you reenter the result
of a previous calculation to make another calculation.
For Example 2, the continuous sequence of steps is:
E X A M P L E 3 A loan for 36 months, with a finance charge of $1,276.50, is paid
in full with 15 payments remaining. Find the finance charge to be refunded.
sum of the digits for number of payments remaining
sum of the digits for total number of payments
sum of digits from 1 through 15
15 * 16 , 2 = Q 120
=
sum of digits from 1 through 36
36 * 37 , 2 = Q 666
120
Refund fraction =
666
Finance charge refund = finance charge * refund fraction
120
= $1,276.50 a
b
666
= $230
Calculator sequence: 1276.50 * 120 , 666 =
Refund fraction =
The finance charge refund is $230.
STOP AND CHECK
1. A loan for 12 months with interest of $397.85 is paid in full
with five payments remaining. What is the refund fraction
for the interest refund?
2. A loan for 48 months has interest of $2,896 and is paid in
full with 18 months remaining. What is the refund fraction
for the interest refund?
3. A loan for 36 months requires $1,798 interest. The loan is
paid in full with 6 months remaining. How much interest is
refunded?
4. Ruth Brechner borrowed money to purchase a retail
business. The 60-month loan had $4,917 interest. Ruth’s
business flourished and she repaid the loan after 50 months.
How much interest refund did she receive?
12-2 SECTION EXERCISES
SKILL BUILDERS
2. Find the refund fraction on an 18-month loan if it is paid
off with 8 months remaining.
3. Find the interest refund on a 36-month loan with interest of
$2,817 if the loan is paid in full with 9 months remaining.
4. Stephen Helba took out a loan to purchase a computer. He
originally agreed to pay off the loan in 18 months with a
finance charge of $205. He paid the loan in full after 12
payments. How much finance charge refund should he get?
ISBN 1-256-64971-6
1. Calculate the refund fraction for a 60-month loan that is
paid off with 18 months remaining.
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
435
APPLICATIONS
5. John Paszel took out a loan for 48 months but paid it in full
after 28 months. Find the refund fraction he should use to
calculate the amount of his refund.
6. If the finance charge on a loan made by Marjorie Young is
$1,645 and the loan is to be paid in 48 monthly payments,
find the finance charge refund if the loan is paid in full with
28 months remaining.
7. Phillamone Berry has a car loan with a company that
refunds interest using the rule of 78 when loans are paid in
full ahead of schedule. He is using an employee bonus to
pay off his Traverse, which is on a 42-month loan. The total
interest for the loan is $2,397, and he has 15 more
payments to make. How much finance charge will he get
credit for if he pays the loan in full immediately?
8. Dwayne Moody purchased a four-wheel drive vehicle and
is using severance pay from his current job to pay off the
vehicle loan before moving to his new job. The total
interest on the 36-month loan is $3,227. How much finance
charge refund will he receive if he pays the loan in full with
10 more payments left?
12-3 OPEN-END CREDIT
LEARNING OUTCOMES
1. Find the finance charge and new balance using the average daily balance method.
2. Find the finance charge and new balance using the unpaid or previous month’s balance.
Line-of-credit accounts: a type of open-end
loan.
Open-end loans are often called line-of-credit accounts. While a person or company is paying
off loans, that person or company may also be adding to the total loan account by making a new
purchase or otherwise borrowing money on the account.
For example, you may want to use your Visa card to buy new textbooks even though you still
owe for clothes bought last winter. Likewise, a business may use an open-end credit account to
buy a new machine this month even though it still owes the bank for funds used to pay a major
supplier six months ago.
Nearly all open-end accounts are billed monthly. Interest rates are most often stated as annual rates. The Fair Credit and Charge Card Disclosure Act of 1988 and updates passed since
that time specify the required details that must be disclosed for charge cards and line-of-credit
accounts. These details include all fees, grace period, how finance charges are calculated, how
late fees are assessed, and so on. While this act addresses the disclosure of fees and charges, The
Credit Card Act of 2009 (effective February 22, 2010) imposes regulations on credit card issuers
in an attempt to stop them from unfairly taking advantage of consumers.
1 Find the finance charge and new balance using the average
daily balance method.
Average daily balance: the average of the daily
balances for each day of the billing cycle.
436
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
Billing cycle: the days that are included on a
statement or bill.
Many lenders determine the finance charge using the average daily balance method. In this
method, the daily balances of the account are determined, and then the sum of these balances is
divided by the number of days in the billing cycle. This average daily balance is next multiplied
by the monthly interest rate to find the finance charge for the month.
Even though open-end credit accounts are billed monthly, the monthly period may not coincide with the first and last days of a calendar month. To spread out the workload for the billing
department, each account is given a monthly billing cycle. The billing cycle is the days that are
included on a statement or bill. This cycle can start on any day of a month. For example, a billing
cycle may start on the 22nd of one month and end on the 21st of the next month. This means that
the number of days of a billing cycle will vary from month to month based on the number of days
in the months involved.
HOW TO
Find the average daily balance
1. Find the daily unpaid balance for each day in the billing cycle.
(a) Find the total purchases and cash advances charged to the account during the day.
(b) Find the total credits (payments and adjustments) credited to the account during the day.
(c) To the previous daily unpaid balance, add the total purchases and cash advances for the
day (from step 1a). Then subtract the total credits for the day (from step 1b).
Daily unpaid balance = previous daily unpaid balance + total purchases and cash
advances for the day - total credits for the day
2. Add the unpaid balances from step 1 for each day of the billing cycle, and divide the sum by
the number of days in the cycle.
Average daily balance =
HOW TO
sum of daily unpaid balances
number of days in billing cycle
Find the finance charge using the average daily balance
1. Determine the decimal equivalent of the rate per period.
2. Multiply the average daily balance by the decimal equivalent of the rate per period.
TIP
When Does the Balance
Change?
In most cases, if a transaction
reaches a financial institution at any
time during the day, the transaction
is posted and the balance is updated
at the end of the business day.
Thus, the new balance takes effect
at the beginning of the next day.
Calculations on the day’s unpaid
balance are made on the end-ofday amount (same as beginning of
next day).
E X A M P L E 1 Use the chart showing May activity in the Hodge’s Tax Service
charge account to determine the average daily balance and finance charge for the month. The
bank’s finance charge is 1.5% per month on the average daily balance.
Date transaction posted
May 1
May 7
May 10
May 13
May 20
May 23
Transaction
Billing date
Payment
Purchase (pencils)
Purchase (envelopes)
Cash advance
Purchase (business forms)
Transaction amount
Balance $122.70
25.00
12.00
20.00
50.00
100.00
To find the average daily balance, we must find the unpaid balance for each day, add these balances, and divide by the number of days.
Day
1
2
3
4
5
6
7
8
9
10
Total:
Balance
122.70
122.70
122.70
122.70
122.70
122.70
97.70 (122.70 - 25)
97.70
97.70
109.70 (97.70 + 12)
$5,322.70
Day
11
12
13
14
15
16
17
18
19
20
Balance
109.70
109.70
129.70 (109.70 + 20)
129.70
129.70
129.70
129.70
129.70
129.70
179.70 (129.70 + 50)
Average Daily Balance:
Day
21
22
23
24
25
26
27
28
29
30
31
Balance
179.70
179.70
279.70 (179.70 + 100)
279.70
279.70
279.70
279.70
279.70
279.70
279.70
279.70
$171.70
ISBN 1-256-64971-6
The average daily balance can also be determined by grouping days that have the same balance.
For the first six days, May 1–May 6, there is no activity, so the daily unpaid balance is the previous unpaid balance of $122.70. The sum of daily unpaid balances for these six days, then, is
122.70(6).
$122.70(6) = $736.20
On May 7 there is a payment of $25, which reduces the daily unpaid balance.
$122.70 - $25 = $97.70
The new balance of $97.70 holds for the three days (May 7, 8, and 9) until May 10.
$97.70(3) = $293.10
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
437
Continue doing this until you get to the end of the cycle. The calculations can be organized in a
chart.
Date
May 1–May 6
May 7–May 9
May 10–May 12
May 13–May 19
May 20–May 22
May 23–May 31
Daily unpaid
balance
$122.70
97.70
109.70
129.70
179.70
279.70
Change
-$25.00
+10.00
+20.00
+50.00
+100.00
Number
of days
6
3
3
7
3
9
Total 31
Partial sum
$ 736.20
293.10
329.10
907.90
539.10
2,517.30
$5,322.70
Divide the sum of $5,322.70 by the 31 days.
sum of daily unpaid balances
number of days
$5,322.70
= $171.70
=
31
Average daily balance =
To find the interest, multiply the average daily balance by the monthly interest rate of 1.5%.
Finance charge = $171.70(0.015)
= $2.58
The average daily balance is $171.70 and the finance charge is $2.58.
STOP AND CHECK
Account Number
xxxx-xxxx-xxxx-xxxx
Credit Limit
$5,000
Posting
Date
Transaction
Date
9/26
9/24
10/6
Available Credit
$4,212.28
Description
Billing Period
9/24/12 to 10/24/12
Amount
CR–Credit PY–Payment
The Store Oxford MS
$11.93
CR
10/02
Chili's Oxford MS
$15.24
CR
10/8
10/06
Durall St Cloud FL
$86.98
CR
10/10
10/10
Payment Received–Thank You
$927.86
PY
10/14
10/12
Foley's Knitwear San Antonio TX
$113.19
CR
10/20
10/16
Red Lobster Tupelo MS
$22.88
CR
10/20
10/19
JC Penny Co Oxford MS
$47.36
CR
Finance Charge
Average
Daily
Balance
Monthly
Periodic
Rate
Purchases
1.0750%
Cash Advances
1.0750%
$
1,406.54
Purchases
+
297.58
Other Charges
+
.00
Variable
Cash Advances
+
0.00
12.90%
Credits
–
.00
Finance
Charge
Payments
–
927.86
Variable
Late Charges
+
.00
12.90%
Finance Charges
+
11.46
New Balance
$
787.72
FIGURE 12-1
438
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
$0.00
Balance
Previous Balance
Corresponding
Annual
Percentage
Rate
Use the statement in Figure 12-1 for Exercises 1–4.
1. Make a table showing the unpaid balance for each day in
the billing period.
2. Find the average daily balance for the month.
3. Find the finance charge for the month.
4. Find the new balance for the month.
2 Find the finance charge and new balance using the unpaid
or previous month’s balance.
Not all open-end credit accounts use the average daily balance method for determining the
monthly finance charge. Another method uses the unpaid or previous month’s balance as the
basis for determining the finance charge. In this method, the new purchases or payments made
during a month do not affect the finance charge for that month.
HOW TO
Find the finance charge and new balance using the unpaid or
previous month’s balance
Finance charge:
1. Find the monthly rate.
Monthly rate =
Annual percentage rate
12
2. Multiply the unpaid or previous month’s balance by the monthly rate.
Finance charge = Unpaid balance * Monthly rate
New balance:
1. Total the purchases and cash advances for the billing cycle.
2. Total the payments and credits for the billing cycle.
3. Adjust the unpaid balance of the previous month using the totals in steps 1 and 2.
ISBN 1-256-64971-6
New balance Previous balance Finance charge Purchases and cash advances Payments and credits
EXAMPLE 2
Hanna Stein has a department store revolving credit account with
an annual percentage rate of 21%. Her unpaid balance for her March billing cycle is $285.45.
During the billing cycle she purchased shoes for $62.58 and a handbag for $35.18. She returned
a blouse that she had purchased in the previous billing cycle, received a credit of $22.79, and she
made a payment of $75. If the store uses the unpaid balance method, what are the finance charge
and the new balance?
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
439
Monthly rate:
Annual percentage rate
12
21%
0.21
Monthly rate =
=
= 0.0175
12
12
Monthly rate =
Finance charge:
Finance charge = Unpaid balance * Monthly rate
Finance charge = $285.45(0.0175) = $5.00
Rounded from $4.995375
New balance:
Total purchases and cash advances = $62.58 + $35.18 = $97.76
Total payments and credits = $75 + $22.79 = $97.79
New balance = Previous balance + Finance charge + Purchases and cash advances Payments and credits
New balance = $285.45 + $5 + $97.76 - $97.79 = $290.42
STOP AND CHECK
1. Shakina Brewster has a Target revolving credit account that
has an annual percentage rate of 18% on the unpaid
balance. Her unpaid balance for the July billing cycle is
$1,285.96. During the billing cycle, Shakina purchased
groceries for $98.76 and received $50 in cash. She
purchased linens for $46.98. Shakina made a payment of
$135. Find the finance charge and new balance if Target
uses the unpaid balance method.
2. Shameka Brown has a Best Buy Stores revolving credit
account that has an annual percentage rate of 15% on the
unpaid balance. Her unpaid balance for the October billing
cycle is $2,531.77. During the billing cycle, Shameka
purchased movies for $58.63 and received $70 in cash.
She purchased a camera for $562.78 and returned a printer
purchased in September for credit of $85.46. Shameka
made a payment of $455. Find the finance charge and new
balance if Best Buy uses the unpaid balance method.
3. Dallas Hunsucker has a Master Card account with an
annual percentage rate of 24%. The unpaid balance for his
January billing cycle is $2,094.54. During the billing cycle
he made grocery purchases of $65.82, $83.92, $12.73, and
gasoline purchases of $29.12 and $28.87. He made a
payment of $400. If the account applies the unpaid balance
method, what were the finance charge and the new balance?
4. Ryan Bradley has a Visa Card with an introductory annual
percentage rate of 9%. The unpaid balance for his February
billing cycle is $245.18. During the billing cycle he
purchased fresh flowers for $45.00, candy for $22.38, and
gasoline for $36.53. He made a payment of $100 and had a
return for credit of $74.93. If the account applies the unpaid
balance method, what are the finance charge and the new
balance?
12-3 SECTION EXERCISES
SKILL BUILDERS
2. Find the monthly interest rate if the annual rate is 15.6%.
3. A credit card has an average daily balance of $2,817.48 and
the monthly periodic rate is 1.325%. What is the finance
charge for the month?
4. What is the finance charge on a credit card account that has
an average daily balance of $5,826.42 and the monthly
interest rate is 1.55%?
440
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
1. What is the monthly interest rate if an annual rate is 13.8%?
APPLICATIONS
5. Jim Riddle has a credit card that charges 10% annual
interest on the monthly average daily balance for the billing
cycle. The current billing cycle has 29 days. For 15 days his
balance was $2,534.95. For 7 days the balance was
$1,534.95. And for 7 days the balance was $1,892.57. Find
the average daily balance. Find the amount of interest.
6. Suppose the charge account of Strong’s Mailing Service at
the local supply store had a 1.8% interest rate per month on
the average daily balance. Find the average daily balance if
Strong’s had an unpaid balance on March 1 of $128.50, a
payment of $20 posted on March 6, and a purchase of $25.60
posted on March 20. The billing cycle ends March 31.
7. Using Exercise 6, find Strong’s finance charge on April 1.
8. Make a chart to show the transactions for Rick Schiendler’s
credit card account in which interest is charged on the
average daily balance. The cycle begins on May 4, and the
cycle ends on June 3. The beginning balance is $283.57. A
payment of $200 is posted on May 18. A charge of $19.73
is posted on May 7. A charge of $53.82 is posted on May
12. A charge of $115.18 is posted on May 29. How many
days are in the cycle? What is the average daily balance?
9. Rick is charged 1.42% per period. What is the finance
charge for the cycle?
12. Chaundra Mixon has a Master Card with an annual
percentage rate of 19.8%. The unpaid balance for her
August billing cycle is $675.21. During the billing cycle
she purchased shoes for $87.52, a suit for $132.48, and a
wallet for $28.94. She made a payment of $225. If the
account applies the unpaid balance method, what are the
finance charge and the new balance?
ISBN 1-256-64971-6
11. Jamel Cisco has a Visa Card with an annual percentage rate
of 16.8%. The unpaid balance for his June billing cycle is
$1,300.84. During the billing cycle he purchased a printer
cartridge for $42.39, books for $286.50 and gasoline for
$16.71. He made a payment of $1,200. If the account
applies the unpaid balance method, what are the finance
charge and the new balance?
10. What is the beginning balance for the next cycle of Rick’s
credit card account?
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
441
SUMMARY
Learning Outcomes
CHAPTER 12
What to Remember with Examples
Section 12-1
1
Find the amount financed, the
installment price, and the finance
charge of an installment loan.
(p. 426)
1. Find the amount financed: Subtract the down payment from the cash price.
Amount financed = cash price - down payment
2. Find the installment price: Add the down payment to the total of the installment payments.
Installment price = total of installment payments + down payment
Find the installment price of a computer that is paid for in 24 monthly payments of $113 if a
down payment of $50 is made.
(24)($113) + $50 = $2,712 + $50 = $2,762
Find the finance charge of an installment loan:
Subtract the cash price from the installment price.
Finance charge = installment price - cash price
If the cash price of the computer in the previous example was $2,499, how much is the
finance charge?
$2,762 - $2,499 = $263
2
Find the installment payment of
an installment loan. (p. 427)
1. Find the total of the installment payments: Subtract the down payment from the installment
price.
Total of installment payments = installment price - down payment
2. Divide the total of installment payments by the number of installment payments.
Installment payment =
total of installment payments
number of payments
Find the monthly payment on a computer if the cash price is $3,285. A 14% interest rate is
charged on the cash price, and there are 12 monthly payments.
$3,285(0.14)(1) = $459.90
Installment price = $3,285 + $459.90 = $3,744.90
$3,744.90
Monthly payment =
= $312.08
12
A computer has an installment price of $2,187.25 when financed over 18 months. If a $100
down payment is made, find the monthly payment.
$2,187.25 - $100 = $2,087.25
$2,087.25
= $115.96
Monthly payment =
18
Find the estimated annual
percentage rate (APR) using a
table. (p. 428)
1. Find the interest per $100 of amount financed: Divide the finance charge by the amount
financed and multiply by $100.
Interest per $100 =
442
total finance charge
* $100
amount financed
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
3
2. Find the row corresponding to the number of monthly payments. Move across the row to
find the number closest to the value from step 1. Read up the column to find the annual
percentage rate for that column. If the result in step 1 is exactly half way between two
table values use the higher rate or a rate half way between the two rates can be used.
Find the annual percentage rate on a loan of $500 that is repaid in 36 monthly installments.
The interest for the loan is $95.
Interest per $100 =
$95
($100) = $19
$500
In the row for 36 months, move across to 19.14 (nearest to 19). APR is at the top of the
column, 11.75%.
Section 12-2
1
Find the interest refund using the
rule of 78. (p. 433)
Find the refund fraction.
1. The numerator is the sum of the digits from 1 through the number of months remaining of a
loan paid off before it was due.
2. The denominator is the sum of the digits from 1 through the original number of months of
the loan.
3. The original fraction, the reduced fraction or the decimal equivalent of the fraction can be
used.
Find the refund fraction on a loan that has a total finance charge of $892 and was made for
24 months. The loan is paid in full with 10 months (payments) remaining.
sum of digits from 1 to the number of periods remaining
sum of digits from 1 through original number of periods
sum of 1 to 10
=
sum of 1 to 24
11
55
or
or 0.1833333333
=
300 60
Refund fraction =
Find the interest refund using the rule of 78.
1. Find the refund fraction.
2. Multiply the total interest by the refund fraction.
Interest refund = total interest * refund fraction
Find the interest refund for the previous example.
Interest refund = $892 a
11
b = $163.53 892 * 11 , 60 = Q 163.5333333
60
Section 12-3
1
Find the finance charge and new
balance using the average daily
balance method. (p. 436)
1. Find the daily unpaid balance for each day in the billing cycle.
(a) Find the total purchases and cash advances charged to the account during the day.
(b) Find the total credits (payments and adjustments) credited to the account during the day.
(c) To the previous daily unpaid balance, add the total purchases and cash advances for the
day (from step 1a). Then subtract the total payments for the day (from step 1b).
ISBN 1-256-64971-6
Daily unpaid balance = previous daily unpaid balance + total purchases
and cash advances for the day - total credits for the day
2. Add the unpaid balances from step 1 for each day of the billing cycle, and divide the sum by
the number of days in the cycle.
Average daily balance =
sum of daily unpaid balances
number of days in billing cycle
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
443
A credit card has a balance of $398.42 on September 14, the first day of the billing cycle. A
charge of $182.37 is posted to the account on September 16. Another charge of $82.21 is
posted to the account on September 25. The amount of a returned item ($19.98) is posted to
the account on October 10 and a payment of $500 is made on October 12. The billing period
ends on October 13. Find the average daily balance.
Date
September 14–15
September 16–24
September 25–October 9
October 10–11
October 12–13
Change
+$182.37
+82.21
-19.98
-500.00
Daily Unpaid
Balance
$398.42
580.79
663.00
643.02
143.02
Number
of Days
2 days
9 days
15 days
2 days
2 days
Total 30 days
Partial Sum
$ 796.84
5,227.11
9,945.00
1,286.04
286.04
$17,541.03
Average daily balance = $17,541.03 , 30 = $584.70
Find the finance charge using the average daily balance:
1. Determine the decimal equivalent of the rate per period.
2. Multiply the average daily balance by the decimal equivalent of the rate per period.
Find the finance charge for the average daily balance in the preceding example if the
monthly rate is 1.3%.
Finance charge = $584.70(0.013) = $7.60
2
Find the finance charge and new
balance using the unpaid or
previous month’s balance. (p. 439)
Finance charge:
1. Find the monthly rate.
Monthly rate =
Annual percentage rate
12
2. Multiply the unpaid or previous month’s balance by the monthly rate.
Finance charge = Unpaid balance * Monthly rate
New balance:
1. Total the purchases and cash advances for the billing cycle.
2. Total the payments and credits for the billing cycle.
3. Adjust the unpaid balance of the previous month using the totals in steps 1 and 2.
New balance = previous balance + finance charge + purchases and cash advances
- payments and credits
Dakota Beasley has a Visa account with an annual percentage rate of 24%. Her unpaid balance for her September billing cycle is $381.15. During the billing cycle she made gasoline
purchases of $25.18, $18.29, $22.75, and $19.12. She made a payment of $100. If the account applies the unpaid balance method, what is the finance charge and the new balance?
Monthly rate =
Monthly rate =
444
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
Finance charge =
Finance charge =
Total purchases =
=
Payments =
New balance =
=
Annual percentage rate
12
0.24
24%
=
= 0.02
12
12
Unpaid balance * Monthly rate
$381.15(0.02) = $7.62 Rounded from $7.623
$25.18 + $18.29 + $22.75 + $19.12
$85.34
$100
$381.15 + $7.62 + $85.34 - $100
$374.11
NAME
DATE
EXERCISES SET A
CHAPTER 12
1. Find the installment price of a notebook computer system
bought on the installment plan with $250 down and 12 payments of $111.33.
2. Find the monthly payment on a water bed if the installment
price is $1,050, the down payment is $200, and there are 10
monthly payments.
3. If the cash price of a refrigerator is $879 and a down payment
of $150 is made, how much is to be financed?
4. Find the refund fraction for a 60-month loan if it is paid in full
with 22 months remaining.
Use the rule of 78 to find the finance charge (interest) refund in each of the following.
Number of
monthly payments
Remaining
payments
EXCEL 5. $238
12
4
EXCEL 6. $2,175
24
10
EXCEL 7. $896
18
4
ISBN 1-256-64971-6
Finance
charge
Interest
refund
8. The finance charge on a copier was $1,778. The loan for the
copier was to be paid in 18 monthly payments. Find the finance charge refund if it is paid off in eight months.
9. Becky Whitehead has a loan with $1,115 in finance charges,
which she paid in full after 10 of the 24 monthly payments.
What is her finance charge refund?
10. Alice Dubois was charged $455 in finance charges on a loan
for 15 months. Find the finance charge refund if she pays off
the loan in full after 10 payments.
11. Find the finance charge refund on a 24-month loan with
monthly payments of $103.50 if you decide to pay off the loan
with 10 months remaining. The finance charge is $215.55.
12. If you purchase a fishing boat for 18 monthly payments of
$106 and an interest charge of $238, how much is the refund
after 10 payments?
13. Find the interest on an average daily balance of $265 with an
interest rate of 112%.
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
445
14. Find the finance charge on a credit card with an average daily
balance of $465 if the rate charged is 1.25%.
15. Use the following activity chart for a credit card to find the
unpaid balance on November 1. The billing cycle ended on
October 31, and the finance charge is 1.5% of the average
daily balance.
Date posted
October 1
October 8
October 11
October 16
October 21
Activity
Billing date
Purchase
Payment
Purchase
Purchase
Amount
Previous balance $426.40
41.60
70.00
31.25
26.80
Use Table 12-1 to find the annual percentage rate (APR) for the following exercises.
16. Find the annual percentage rate on a loan of $1,500 for
18 months if the loan requires $190 interest and is repaid
monthly.
17. Find the annual percentage rate on a loan of $3,820 if the
monthly payment is $130 for 36 months.
18. A vacuum cleaner was purchased on the installment plan with
12 monthly payments of $36.98 each. If the cash price was
$415 and there was no down payment, find the annual percentage rate.
19. A merchant charged $420 in cash for a dining room set that
could be bought for $50 down and $40.75 per month for
10 months. What is the annual percentage rate?
20. An electric mixer was purchased on the installment plan for
a down payment of $60 and 11 monthly payments of $11.05
each. The cash price was $170. Find the annual percentage
rate.
21. A computer was purchased by paying $50 down and 24
monthly payments of $65 each. The cash price was $1,400.
Find the annual percentage rate to the nearest tenth of a
percent.
ISBN 1-256-64971-6
446
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
NAME
DATE
EXERCISES SET B
CHAPTER 12
1. A television set has been purchased on the installment plan
with a down payment of $120 and six monthly payments of
$98.50. Find the installment price of the television set.
2. A dishwasher sold for a $983 installment price with a down
payment of $150 and 12 monthly payments. How much is
each payment?
3. What is the cash price of a chair if the installment price is
$679, the finance charge is $102, and there was no down
payment?
4. Find the refund fraction for a 42-month loan if it is paid in full
with 16 months remaining.
Use the rule of 78 to find the finance charge refund in each of the following.
Finance
charge
Number of
monthly payments
Remaining
payments
EXCEL 5. $1,076
18
6
EXCEL 6. $476
12
5
EXCEL 7. $683
15
11
ISBN 1-256-64971-6
8. Find the refund fraction on a 48-month loan if it is paid off
after 20 months.
Interest
refund
9. Lanny Jacobs made a loan to purchase a computer. Find the
refund due on this loan with interest charges of $657 if it is
paid off after paying 7 of the 12 monthly payments.
10. Suppose you have borrowed money that is being repaid at $45
a month for 12 months. What is the finance charge refund after
making eight payments if the finance charge is $105?
11. You have purchased a new stereo on the installment plan. The
plan calls for 12 monthly payments of $45 and a $115 finance
charge. After nine months you decide to pay off the loan. How
much is the refund?
12. The interest for an automobile loan is $2,843. The automobile
is financed for 36 monthly payments, and interest refunds are
made using the rule of 78. How much interest should be
refunded if the loan is paid in full with 22 months still
remaining?
13. Find the finance charge on $371 if the interest charge is 1.4%
of the average daily balance.
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
447
14. A new desk for an office has a cash price of $1,500 and can
be purchased on the installment plan with a 12.5% finance
charge. The desk will be paid for in 12 monthly payments.
Find the amount of the finance charge, the total price, and the
amount of each monthly payment, if there was no down
payment.
15. On January 1 the previous balance for Lynn’s charge account
was $569.80. On the following days, purchases were posted:
January 13
January 21
$38.50
$44.56
jewelry
clothing
On January 16 a $50 payment was posted. Using the average
daily balance method, find the finance charge and unpaid
balance on February 1 if the bank charges interest of 1.5% per
month.
Use Table 12-1 to find the annual percentage rate for the following exercises.
16. Find the annual percentage rate on a loan for 25 months if the
amount of the loan without interest is $300. The loan requires
$40 interest.
17. Find the annual percentage rate on a loan of $700 without
interest with 12 monthly payments. The loan requires $50
interest.
18. A queen-size brass bed costs $1,155 and is financed with
monthly payments for three years. The total finance charge is
$415.80. Find the annual percentage rate.
19. John Edmonds borrowed $500. He repaid the loan in
22 monthly payments of $26.30 each. Find the annual
percentage rate.
20. A loan of $3,380 was paid back in 30 monthly payments with
an interest charge of $620. Find the annual percentage rate.
21. A 6 * 6 color enlarger costs $1,295 and is financed with
monthly payments for two years. The total finance charge is
$310.80. Find the annual percentage rate.
ISBN 1-256-64971-6
448
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
NAME
PRACTICE TEST
DATE
CHAPTER 12
1. Find the finance charge on an item with a cash price of $469 if the
installment price is $503 and no down payment was made.
2. An item with a cash price of $578 can be purchased on the installment plan in 15 monthly payments of $46. Find the installment price
if no down payment was made. Find the finance charge.
3. The installment price of a Bosch stainless steel refrigerator is
$2,199.99 for an 18-month loan. If a $300 down payment has been
made, find the installment payment.
4. The installment price of an Electrolux front-load washer is $1,299.90.
What is the installment payment if a down payment of $295 is made
and the loan is for 12 months?
5. A copier that originally cost $300 was sold on the installment plan at
$28 per month for 12 months. Find the installment price if no down
payment was made. Find the finance charge.
6. Use Table 12-1 to find the annual percentage rate for the loan in
Exercise 3.
7. Use Table 12-1 to find the APR on a loan of $3,000 for three years if
the loan had $810 interest and was repaid monthly.
8. Find the interest on an average daily balance of $165 if the monthly
interest rate is 134%.
10. Find the interest refunded on a 15-month loan with total interest of
$72 if the loan is paid in full with six months remaining.
11. Find the annual percentage rate on a loan of $1,600 for 24 months if
$200 interest is charged and the loan is repaid in monthly payments.
Use Table 12-1.
12. Find the annual interest rate on a loan that is repaid monthly for
26 months if the amount of the loan is $1,075. The interest charged
is $134.85.
13. Office equipment was purchased on the installment plan with
12 monthly payments of $11.20 each. If the cash price was $120
and there was no down payment, find the annual percentage rate.
14. A canoe has been purchased on the installment plan with a down payment of $75 and 10 monthly payments of $80 each. Find the installment price of the canoe.
ISBN 1-256-64971-6
9. Find the yearly rate of interest on a loan if the monthly rate is 2%.
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
449
15. Find the monthly payment when the installment price is $2,300, a
down payment of $400 is made, and there are 12 monthly payments.
16. How much is to be financed on a cash price of $729 if a down
payment of $75 is made?
17. Maurice Van Norman made a 48-month loan that has interest of
$1,987. He paid the loan in full with 11 months remaining. The interest is refunded based on the rule of 78. Find the amount of interest to
be refunded.
18. Larry Williams made a 60-month loan that has interest of $2,518.
He paid the loan in full with 21 months remaining. The interest is
refunded based on the rule of 78. Find the amount of interest to be
refunded.
19. A 30-month loan that has interest of $3,987 is paid in full with
7 months remaining. Find the amount of interest to be refunded
using the rule of 78.
20. Use the following activity chart to find the average daily balance,
finance charge, and unpaid balance for July. The monthly interest
rate is 1.75%. The billing cycle has 31 days.
Date Posted
July 1
July 5
July 16
July 26
21. Mary Lawson has a credit card account with an annual percentage
rate of 18.24%. The unpaid balance for her November billing cycle
is $783.56. During the billing cycle she purchased a desk chair for
$134.77 and a floor mat for $82.36. Mary returned a grill purchased
in the previous month for a credit of $186.21 and she made a
payment of $80. If the account applies the unpaid balance method,
what are the finance charge and the new balance?
Activity
Billing date
Payment
Purchase
Purchase
Amount
Previous balance $441.05
$75.00
23.50
31.40
22. Leslie Joiner has a credit card with an annual percentage rate of
17.4%. The unpaid balance for his June billing cycle is $2,156.28.
During the billing cycle he purchased a refrigerator for $989.21 and
a computer for $873.52. Leslie returned clothing purchased in May
for a credit of $215.77 and made a payment of $425. If the account
applies the unpaid balance method, what are the finance charge and
the new balance?
ISBN 1-256-64971-6
450
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
CRITICAL THINKING
1. Explain the mistake in the solution of the problem and correct the
solution.
Dawn Mayhall financed a car and the loan of 42 months
required $3,827 interest. She paid the loan off after making
20 payments. How much interest should be refunded if the rule of
78 is used?
Solution:
Refund fraction =
210
903
210
($3,827) = $890
903
CHAPTER 12
2. Explain the mistake in the solution and correct the solution.
Ava Landry agreed to pay $2,847 interest for a 36-month loan to
redecorate her greeting card shop. However, business was better than
expected and she repaid the loan with 16 months remaining. If the
rule of 78 was used, how much interest should she get back?
Solution:
16
($2,847) = $1,265.33
36
Thus, $1,265.33 should be refunded.
Thus, $890 should be refunded.
3. Arrange the consecutive numbers from 1 to 10 in ascending order, then
in descending order, so that 1 and 10, 2 and 9, 3 and 8, and so on, align
vertically. Add vertically. Find the grand total. Finally divide the grand
total by 2. Compare the result to the sum of digits 1 through 10.
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
4. Explain why finding the sum of consecutive numbers by using the
process in Exercise 3 requires that the product be divided by 2.
5. Explain why the formula for finding the sum of consecutive numbers
requires the product of the largest number and one more than the
largest number rather than one less than the largest number.
6. Give three examples of finding the sum of consecutive odd numbers
beginning with 1.
ISBN 1-256-64971-6
Challenge Problem
It pays to read the details! Bank One Delaware offers a Platinum Visa Credit Card to qualifying persons with an introductory 0% fixed APR on all purchases
and balance transfers and, after the 12-month introductory period, a low variable APR on purchases and balance transfers at a current annual rate of 8.99%.
However, the default rate is 24.99% APR. A default occurs if the minimum payment is not received by the due date on the billing statement or if your balance ever exceeds your credit limit. Find the difference in just one month’s interest on an average daily balance of $1,000 if the payment is not received by
the due date.
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
451
CASE STUDIES
12-1 Know What You Owe
Nancy Tai has recently opened a revolving charge account with MasterCard. Her credit limit is
$1,000, but she has not charged that much since opening the account. Nancy hasn’t had the time to
review her monthly statements promptly as she should, but over the upcoming weekend she plans to
catch up on her work. She has been putting it off because she can’t tell how much interest she paid or
the unpaid balance in November. She spilled watercolor paint on that portion of the statement.
In reviewing November’s statement she notices that her beginning balance was $600 and that
she made a $200 payment on November 10. She also charged purchases of $80 on November 5, $100
on November 15, and $50 on November 30. She paid $5.27 in interest the month before. She does remember, though, seeing the letters APR
and the number 16%. Also, the back of her statement indicates that interest was charged using the average daily balance method, including
current purchases, which considers the day of a charge or credit.
1. Find the unpaid balance on November 30 before the interest is charged.
2. Assuming a 30-day period in November find the average daily balance.
3. Calculate the interest for November.
4. What was the unpaid balance for November after interest is charged?
Source: Adapted from Winger and Frasca, Personal Finance: An Integrated Approach, 6th edition, Upper Saddle River, NJ: Prentice Hall, p. 162.
12-2 Massage Therapy
It was time to expand her massage therapy business, and Arminte had finally found a commercial space
that met her needs. With room for herself and the two new massage therapists she planned to hire, and
adjacent to a chiropractor’s office, the space was everything that she had hoped for. Now all she needed
was to finalize purchases for three massage rooms, furniture for the reception area, various artwork, and
miscellaneous supplies. Arminte started to make a list of massage equipment: 3 tables at $1,695 each;
3 stools at $189 each; a portable massage chair for $399; and the list went on—bolsters, pillows, sheets,
table warmers, and music. By the time Arminte was finished, her massage equipment alone totaled
$7,644.25, including sales tax. The supplier offered in-house financing of 24 monthly payments at
$325.33 per month, with a 10% down payment.
1. Find the amount financed, installment price, and the finance charge presuming Arminte goes with
the financing available through her supplier.
452
CHAPTER 12
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
ISBN 1-256-64971-6
2. Use Table 12-1 to find the annual percentage rate (APR) of the financing.
3. If Arminte takes the financing but pays the balance in full with 9 months remaining, what is the amount of the finance charge to be
refunded using the rule of 78?
ISBN 1-256-64971-6
4. Arminte had recently opened a revolving charge account with MasterCard, to pick up some miscellaneous supplies for her business. Her
credit limit is $1,500, with 18% APR. Her beginning balance for the month of April was $440, and she made a payment of $60, which
was received on April 10. She purchased massage oil for $240 on April 6, office supplies for $68.45 on April 14, a CD player for
$129.44 on April 20, and $25 in gas on April 27. Arminte’s statement indicates that interest is charged using the average daily balance
method, including current purchases, which considers the day of a charge or credit. Assuming a 30-day period in April, find the average
daily balance and the interest for April.
CONSUMER CREDIT
Business Math, Ninth Edition, by Cheryl Cleaves, Margie Hobbs, and Jeffrey Noble. Published by Prentice Hall. Copyright © 2012 by Pearson Education, Inc.
453