Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges

Подождите немного. Документ загружается.

B (30 points) Compute the ordinary interest, the exact interest, and their difference. Round answers to the

nearest cent. (2 points for each correct interest; 1 point for each correct difference)

Ordinary Exact

Principal Rate Time Interest InterestDifference

11. $2,400 4% 180 days

12. $960 7% 45 days

13. $12,000 6% 240 days

14. $1,400 15% 60 days

15. $7,500 8% 225 days

16. $365 4% 30 days

Score for B (30)

$0.02$1.20$1.22

$5.14$369.86$375.00

$0.48$34.52$35.00

$6.58$473.42$480.00

$0.12$8.28$8.40

$0.66$47.34$48.00

264 Part 4 Interest Applications

Assignment 13.1 Continued

$2,400 3 0.04 3 $2,400 3 0.04 3 $48.00 2 $47.34

180

365

180

360

$960 3 0.07 3 $960 3 0.07 3 $8.40 2 $8.28

365

360

$12,000 3 0.06 3 $12,000 3 0.06 3 $480.00 2 $473.42

240

365

240

360

$1,400 3 0.15 3 $1,400 3 0.15 3 $35 2 $34.52

365

360

$7,500 3 0.08 3 $7,500 3 0.08 3 $375 2 $369.86

225

365

225

360

$365 3 0.04 3 $365 3 0.04 3 $1.22 2 $1.20

365

360

C (20 points) In each problem, first find the actual exact simple interest.Then, estimate the interest by as-

suming a 360-day year and round each rate and time to the nearest numbers that will permit the short-

cuts in Table 13-1. Finally, find the difference. Round answers to the nearest cent. (2 points for each cor-

rect estimate and actual interest; 1 point for each correct difference)

Actual

Exact

Principal Rate Time InterestEstimate Difference

17. $925 8.1% 47 days

18. $5,600 3.99% 92 days

19. $2,000 8.95% 123 days

20. $7,500 6.2% 58 days

Score for C (20)

D (30 points) Determine the missing variable by using one of the following formulas:

I 5 P 3 R 3 T, ,,or

For problems 21–25, use a 360-day year. For problems 26–30, use a 365-day year. Round dollar amounts

to the nearest cent. Round interest rates to the nearest of a percent. Find the time in days, rounded to

the nearest whole day. (3 points for each correct answer)

Principal Rate Time Interest

21. 11% 240 days $352.00

22. $12,500 5% $50.00

29 days

$4,800

T 5

(P 3 R)

R 5

(P 3 T)

P 5

(R 3 T)

$1.11$75.00$73.89

$0.32$60.00$60.32

$0.32$56.00$56.32

$0.40$9.25$9.65

Chapter 13 Simple Interest 265

Assignment 13.1 Continued

$925 3 0.081 3 8% 351% $925 3 0.01 $9.65 2 $9.25

360

365

$7,500 3 0.062 3 6% 3 $7,500 3 0.01 $75.00 2 $73.89

360

5 1%

365

$2,000 3 0.0895 3 9% 353% $2,000 3 0.03 $60.32 2 $60

120

360

123

365

$5,600 3 0.0399 3 4% 351% $5,600 3 0.01 $56.32 2 $56

360

365

year 0.08 3 360 5 28.8, or 29 daysT 5

P 3 R

$50

($12,500 3 0.05)

5 0.08

P 5

R 3 T

$352

a0.11 3

240

360

5 $4,800

Principal Rate Time Interest

23. $600 45 days $6.00

24. $4,260 5.6% 90 days

25. $25,000 4% $625.00

26. 8% 270 days $510.00

27. $3,650 6.75% 136 days

28. $34,950 5.5% $395.00

29. $16,000 90 days $296.00

30. 4.9% 270 days $50.00

Score for D (30)

$1,379.44

7.5%

75 days

$91.80

$8,618.06

225 days

$59.64

266 Part 4 Interest Applications

Assignment 13.1 Continued

R 5

P 3 T

a$600 3

360

5 0.08

I 5 P 3 R 3 T 5 $4,260 3 0.056 3

360

5 $59.64

T 5

(P 3 R)

$625

($25,000 3 0.04)

5 0.625 year 0.625 3 360 5 225 days

P 5

(R 3 T)

$510

a0.08 3

270

365

5 $8,618.06

I 5 P 3 R 3 T 5 $3,650 3 0.0675 35$91.80

136

365

T 5

(P 3 R)

$395

($34,950 3 0.055)

5 0.2055 year 0.2055 3 365 5 75 days

R 5

(P 3 T)

$296

a$16,000 3

365

5 0.0750

P 5

(R 3 T)

$50

a0.049 3

270

365

5 $1,379.44

Chapter 13 Simple Interest 267

Assignment 13.2: Simple Interest Applications

Name

Date Score

A (50 points) Solve each of the following ordinary simple interest problems by using a 360-day year. Find

both the interest dollars and the total amount (i.e., principal plus interest) of the loan. (7 points for each

correct interest; 3 points for each correct amount)

Tom Titus plans to lend $850 to his friend Bill White so that Bill can fly with him to Canada for vacation.

Tom is charging Bill only 3% ordinary simple interest. Bill repays everything, interest plus principal, to

Tom 180 days later. How much does Bill pay?

Interest

Amount

2. Tony Woo and Helen Lee are planning to start a business that will export American food to China. They

estimate that they will need $75,000 to pay for organizational costs, get product samples, and make three

trips to Shanghai. They can borrow the money from their relatives for 4 years. Tony and Helen are willing

to pay their relatives 9% ordinary simple interest. Compute the total amount that Tony and Helen will

owe their relatives in 4 years.

Interest

Amount

3. Carolyn Wilfert owns a temporary services employment agency. Businesses call her when they need to hire

various types of workers for a short period of time. The businesses pay a fee to Carolyn, who pays the

salaries and benefits to the employees. One benefit is that Carolyn will make small, short-term loans to her

employees. After a flood, employee Judy Hillstrom needed to borrow $3,600 to have her house cleaned

and repainted. Judy repaid the loan in 6 months. If Carolyn charged 5% ordinary simple interest, how

much did Judy repay?

Interest

Amount

4. Several years ago, Dick Shanley and Karl Coke formed a partnership to rent musical instruments to school

districts that do not want to own and maintain the instruments. In the spring, they investigate borrowing

$80,000 to buy trumpets and trombones. Because they collect their rental fees in advance, they anticipate

being able to repay the loan in 135 days. How much will they need to repay if the ordinary simple interest

rate is 6.5%?

Interest

Amount

5. Along with her husband, Ruby Williams owns and manages a video game arcade. A manufacturer devel-

oped a new line of games and offered very low interest financing to encourage arcade operators such as

Ruby to install the new games. Ruby was able to finance $60,000 worth of games for 8 months for 5.2%

ordinary simple interest. Calculate how much Ruby will repay.

Interest

Amount

Score for A (50)

$62,080

$2,080

$81,950

$1,950

$3,690

$90

$102,000

$27,000

$862.75

$12.75

Learning Objectives

$850 3 0.03 3

$850 1 $12.75

180

360

$75,000 3 0.09 3 4

$75,000 1 $27,000

$3,600 3 0.05 3

$3,600 1 $90

$80,000 3 0.065 3

$80,000 1 $1,950

135

360

$60,000 3 0.052 3

$60,000 1 $2,080

B (50 points) Solve each of the following exact simple interest problems by using a 365-day year. Find

both the interest dollars and the total amount (i.e., principal plus interest) of the loan. (7 points for each

correct interest; 3 points for each correct amount)

Robert Burke, managing partner of a local transportation company, thinks that the company should

borrow money to upgrade its truck repair facility. After investigating several sources of short-term loans,

Robert determines that the company can borrow $400,000 for 200 days at 5.5% exact simple interest.

If the company agrees to take out this loan, how much will it need to repay at the end of the 200 days?

Interest

Amount

7. Dave Engle, a former teacher, now has a business selling supplemetary educational materials such as

books and computer software to parents and schools. In June, he borrowed $45,000 from his bank to buy

some new educational computer games that he hopes to sell during August and September. The bank’s

rate is 6.25% exact simple interest as long as the time does not exceed half a year. If Dave pays the princi-

pal plus the interest in 120 days, how much will he pay?

Interest

Amount

8. After working in construction for 5 years, Jerry Weekly had saved almost enough money to buy a fishing

boat and move to Alaska to become a commercial fisherman. He still needed $9,500, which his wife could

borrow from her parents until the end of the first fishing season. The parents charged 5% exact simple

interest, and Jerry repaid them after 95 days. How much interest did he pay, and what was the total

amount?

Interest

Amount

9. Bill and Carol Campbell need to purchase two new saws for their retail lumber yard. The company that

sells the saws offers them some short-term financing at the relatively high rate of 11% exact simple inter-

est. They decide to accept the financing offer, but only for $5,000 and only for 45 days. How much will

Bill and Carol repay at the end of the 45 days?

Interest

Amount

10. After working for a large accounting firm for 10 years, Bette Ryan, C.P.A., decided to open her own office.

She borrowed $50,000 at 6.7% exact simple interest. She made enough during the first income tax season

to repay the loan in 219 days. How much did Bette repay?

Interest

Amount

Score for B (50)

$52,010

$2,010

$5,067.81

$67.81

$9,623.63

$123.63

$45,924.66

$924.66

$412,054.79

$12,054.79

268 Part 4 Interest Applications

Assignment 13.2 Continued

$400,000 3 0.055 3

$400,000 1 $12,054.79

200

365

$45,000 3 0.0625 3

$45,000 1 $924.66

120

365

$9,500 3 0.05 3

$9,500 1 $123.63

365

$5,000 3 0.11 3

$5,000 1 $67.81

365

$50,000 3 0.067 3

$50,000 1 $2,010

219

365

Installment

Purchases

Chapter 14 Installment Purchases 269

Learning Objectives

By studying this chapter and completing all assignments, you will be able to:

Convert between annual and monthly interest rates.

Compute simple interest on a monthly basis.

Compute finance charges for credit account purchases.

Compute costs of installment purchases.

Compute effective rates.

Amortize a loan.

Compute the monthly payment on a home mortgage.

Learning Objective

Most individuals today can purchase goods or services on credit if they choose. The

buyer gets immediate possession or immediate service but delays payment. Either the

seller extends the credit or the buyer uses a credit card, or loan, from a third party.

Credit is usually offered for an interest charge, which is usually computed each

month. A summary of the purchases, payments, and interest charges is sent to the

borrower (credit purchaser) each month. It may not be simple to compare the methods

used to compute interest by competing lenders. Some lenders may charge interest on the

average daily balance. Although it is a simple concept, and easy for a computer to calcu-

late, it may be difficult for the purchaser to reconcile when he or she makes many

purchases and/or merchandise returns in a single month.

In addition to interest, a lender may charge additional fees to extend credit or loan

money. These might include items such as loan origination fees, membership fees, credit

check fees, administrative fees, and insurance premiums. All of the fees together are

called finance charges. These additional fees, whether one-time, annual, or monthly,

also make it difficult to compare lenders because each lender could be slightly different.

It is of some help to consumers that there are laws that mandate that lenders must

explain their various fees and rates.

270 Part 4 Interest Applications

Converting Interest Rates

Learning Objective

Convert between annual and

monthly interest rates.

The general concept behind charging for credit purchases is to compute finance charges

on the unpaid balance each month. The formula is still I 5 P 3 R 3 T, where P is the

unpaid balance. However, T is not years or a fraction of a year (as in Chapter 13)—

T is in months, and R, the rate, is a monthly rate. For example, the rate might be 1.5%

per month.

Understanding the relationship between monthly and annual rates is important.

Rule: To convert an annual rate to a monthly rate, divide the annual rate by 12; to

convert a monthly rate to an annual rate, multiply the monthly rate by 12.

EXAMPLE A

a. Convert 9% per year to the equivalent monthly rate.

9% annually 4 12 5 0.75% monthly

b. Convert 0.5% per month to the equivalent annual rate.

0.5% monthly 3 12 5 6% annually

a. Convert an 18% annual rate to the equivalent monthly rate.

Divide the annual rate by 12 to get the monthly rate: 18% 4 12 5 1.5% per month

b. Convert a 1.25% monthly rate to the equivalent annual rate.

Multiply the monthly rate by 12 to get the annual rate: 1.25% 3 12 5 15% per year

✔

CONCEPT CHECK 14.1

In terms of single-payment simple interest, 1.5% per month is identical to 18% per year.

Rule: If the rate is annual, the time must be in years; if the rate is monthly, the time

must be in months.

Chapter 14 Installment Purchases 271

Computing Simple Interest on a Monthly Basis

Compute simple interest on a

monthly basis.

Learning Objective

EXAMPLE B

Compute the simple interest on $1,000 for 2 months at 18% per year, on an annual basis

and on a monthly basis.

Annual: I 5 P 3 R 3 T 5 $1,000 3 0.18 per year 3 year 5 $30

Monthly: 18% per year 5 18% 4 12 5 1.5% per month

I 5 P 3 R 3 T 5 $1,000 3 0.015 per month 3 2 months

5 $30

Reminder: Both computations differ from most of those in Chapter 13, where you

counted the exact number of days and divided by either 360 or 365.

Compute the simple interest on $800 for 3 months at 0.5% per month.

I 5 P 3 R 3 T 5 $800 3 0.5% per month 3 3 months 5 $800 3 0.005 3 3 5 $12

✔

CONCEPT CHECK 14.2

Computing Finance Charges

Compute finance charges for credit

account purchases.

Learning Objective

To enable consumers to compute the total cost of credit, Congress has passed several laws,

beginning with the Consumer Credit Protection Act of 1968 (CCPA). Title I of the CCPA

is known as the Tr uth in Lending Act (TILA). TILA is administered by the Federal Reserve

Board. Among other major legislation, Congress also passed the Consumer Leasing Act of

1976, administered by the Federal Trade Commission, and the Home Ownership and

Equity Protection Act of 1994, administered by the Department of Housing and Urban

Development. All of these require lenders to make certain disclosures to consumers.

Among several mandates, TILA requires creditors to tell consumers these three

things:

1. The total of all finance charges, including interest, carrying charges, insurance, and

special fees

2. The annual percentage rate (APR) of the total finance charge

3. The method by which they compute the finance charge

As noted in the previous section, an annual interest rate is a monthly interest rate

multiplied by 12. However, as the term is used in TILA, the annual percentage rate

(APR) is a specific, defined term that must include all finance charges, not just interest.

14.1 There is much consumer protec-

tion information on different Websites.

For example,you can direct students to

go to http://www.federalreserve.gov,

click on “Consumer Information,”and

click on “Consumer Handbook to

Credit Protection Laws.”Or go to

ttp://www.ftc.gov,click on “For Con-

sumers,”click on “Credit,”and click on

“Rules and Acts.”These Websites do

change,so please try each Website

yourself before advising students to try.

Furthermore, under TILA, lenders are permitted to use more than one method to

compute the APR. Lenders may even use either a 360-day year or a 365-day year.

TILA does not set limits on rates.

As mentioned, TILA does require that total finance charges be stated clearly, that the

finance charges also be stated as an annual percentage rate, and that the method of com-

putation be given. Although the method that is mentioned may be stated clearly, it may

not always be simple for a consumer to calculate. One difficulty might be to determine

the account balance that is to be used in the calculation. A wide variety of methods may

be applied. For example:

1. The finance charge may be based on the amount owed at the beginning of the current

month, ignoring payments and purchases.

2. The finance charge may be based on the amount owed at the beginning of the month,

after subtracting any payments during the month and ignoring purchases.

3. The finance charge may be based on the average daily balance. (Add the unpaid

balance each day; divide the total by the number of days in the month.) Payments are

usually included; new purchases may or may not be included.

4. A variation of the average daily balance method is to compute the interest charge

each day, on a daily basis, and then add all the daily interest charges for the month.

Although the total finance charges, and the annual percentage rate, and the method

of calculation may all be clearly stated, some consumers will have difficulty reconstruct-

ing the interest and finance charges on their bills. A consumer who wants to understand

more can write to the creditor to request a more detailed explanation and even an exam-

ple of how to do the calculations.

Figure 14-1 is the lower portion of a typical statement from a retail store. Examples

C and D illustrate two simple methods used to compute finance charges.

272 Part 4 Interest Applications

14.2 The terminology and calculation

rules of the Truth in Lending Act are

summarized in the Comptroller’s

Handbook on Truth in Lending

published in 1996 by the Office of the

Comptroller of the Currency.You can

find it,or direct students to it,at

http://www.occ.treas.gov/

handbook/til.pdf.

14.3 The term annual percentage rate

has more than one meaning in busi-

ness.It may refer to compound interest

rather than simple interest.In TILA,

however,it has a specific meaning and

may include more than just interest.

14.4 Credit card interest calculations

can be very complex—sometimes

almost impossible for the cardholder

to reconcile.Taking real terms from an

actual credit card statement,yours or

a student’s,may be interesting.It may

be useful or necessary to write to the

issuing company for an example of

how it calculates charges.You may be

able to find the information on the

company’s Website.And even with that

information,the method of calculation

may be difficult to duplicate without a

computer.

EXAMPLE C

Compute the finance charge and the new balance for the statement shown in Figure 14-1

based on the previous balance, $624.12, ignoring all payments, credits, and purchases.

Finance charge 5 $624.12 3 1.5% 3 1 month 5 $9.3618, or $9.36

New balance 5 $624.12 1 $9.36 2 $500.00 2 $62.95 1 $364.45 5 $434.98

Figure 14-1 Retail Statement of Account

BALANCE

IF WE RECEIVE PAYMENT OF THE FULL AMOUNT OF THE NEW BALANCE BEFORE THE NEXT CYCLE‘S CLOSING DATE, SHOWN

ABOVE, YOU WILL AVOID A FINANCE CHARGE NEXT MONTH. THE FINANCE CHARGE, IF ANY, IS CALCULATED ON THE

PREVIOUS BALANCE BEFORE DEDUCTING ANY PAYMENTS OR CREDITS SHOWN ABOVE. THE PERIODIC RATES USED ARE

1.5% OF THE BALANCE ON AMOUNTS UNDER $1,000 AND 1% OF AMOUNTS IN EXCESS OF $1,000, WHICH ARE ANNUAL

PERCENTAGE RATES OF 18% AND 12%, RESPECTIVELY.

FINANCE

CHARGE PAYMENTS CREDITS PURCHASES

NEW

BALANCE

MINIMUM

PAYMENT

CLOSING

DATE

624.12 9.36 500.00 62.95 364.45 434.98 45.00 10-16-09

Chapter 14 Installment Purchases 273

The finance terms given in the charge account statement of Figure 14-1 indicate that the

finance charge, if any, is charged on the previous balance, before deducting payments or

credits or adding purchases. Calculate the finance charge and the unpaid balance if the pre-

vious balance was $2,425.90, the payment was $1,200, there were no credits, and there

were $572.50 in new purchases.

An interest rate of 1.5% applies to the first $1,000 and 1% applies to the excess:

$2,425.90 2 $1,000 5 $1,425.90.

0.015 3 $1,000 5 $15.00

0.01 3 $1,425.90 5 $14.26

Finance charge 5 $15.00 1 $14.26 5 $29.26

New balance 5 $2,425.90 2 $1,200 1 $29.26 1 $572.50 5 $1,827.66

COMPLETE ASSIGNMENT 14.1.

✔

CONCEPT CHECK 14.3

In a credit sale, the buyer pays the purchase price plus credit charges. Usually, the buyer

makes monthly payments called installments. Just as you saw in the previous section,

the method of computing the interest is just as important as the interest rate. Most often,

the interest is based on the unpaid balance and is calculated each month using a monthly

interest rate. Sometimes, the interest may be calculated only once at the beginning using

an annual interest rate, but the interest might be paid in equal installments along with

the principal installments.

EXAMPLE E

Nancy Bjonerud purchases $4,000 worth of merchandise. She will repay the principal in

four equal monthly payments of $1,000 each. She will also pay interest each month on

the unpaid balance for that month, which is calculated at an annual rate of 12%. First,

calculate each of the monthly interest payments. Then, display the results in a table.

Compute costs of installment

purchases.

Learning Objective

EXAMPLE D

Assume that the finance charge in Figure 14-1 is based on the previous balance, less any

payments or credits, but ignores subsequent purchases. Compute the finance charge and

the new balance.

The finance charge is based on $624.12 2 $500.00 2 $62.95 5 $61.17

Finance charge 5 $61.17 3 1.5% 3 1 month 5 $0.91575, or $0.92

New balance 5 $624.12 1 $0.92 2 $500.00 2 $62.95 1 $364.45 5 $426.54

Computing Costs of Installment Purchases