Chapter 3 1 An investor purchased 500 shares of a stock at $19 per share

Exam

Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1)

Find the amount due on a loan of $8,500 at 7.5% simple interest at the end of 4 years.

1)

Use an amortization table to solve the problem. Round to the nearest cent.

2)

A home was purchased 14 years ago for $70,000. The home was financed by paying a 20%

down payment and signing a 25 year mortgage at 8.5% compounded monthly on the

unpaid balance. The market value is now $100,000. The owner wishes to sell the house.

How much equity (to the nearest dollar) does the owner have in the house after making

168 monthly payments?

2)

3)

You have agreed to pay off a $8,000 loan in 30 monthly payments of $298.79 per month.

The interest rate of the loan is 0.75% per month on the unpaid balance. What is the unpaid

balance after 12 monthly payments have been made?

3)

Provide an appropriate response.

4)

How much should you invest now at 6% compounded semiannually to have $8,500 to buy

a car in 2.5 years?

4)

5)

An investor purchased 500 shares of a stock at $19 per share. The commission she paid to

buy the stock was $65 plus 0.3% of the principal amount. Six months later she sold the

stock for $20.50 per share. If she paid the same rate of commission to sell the stock, what

annual rate of interest (annual yield) did she earn on her initial investment (including

purchase price plus commission)? Express your answer as a percentage, correct to one

decimal place.

5)

Solve the problem.

6)

A couple decides on the following savings plan for their child’s college education. When

the child is 6 months old, and every 6 months thereafter, they will deposit $310 into a

savings account paying 9.5% interest compounded semi–annually. After the child’s tenth

birthday, having made 20 such payments, they will stop making deposits and let the

accumulated money earn interest, at the same rate, for 8 more years, until the child is 18

years old and ready for college. How much money (to the nearest dollar) will be in the

account when the child is ready for college?

6)

Solve the problem. Round to the nearest cent as needed.

7)

A child receives a $10,000 gift toward a college education from her grandparents on her

first birthday. How much money will it be worth in 17 years if it is invested at 8.25%

compounded quarterly? Round your answer to the nearest cent.

7)

Use an amortization table to solve the problem. Round to the nearest cent.

8)

A $90,000 home was financed by making a 20% down payment and signing a 30–year

mortgage at 6.25% annual interest compounded monthly for the unpaid balance. The first

payment is $443.32. How much of the first month’s payment will apply towards reducing

the principal?

8)

9)

A $7,000 debt is to be amortized in 15 equal monthly payments of $504.87 at 1.00% interest

per month on the unpaid balance. What is the unpaid balance after the second payment?

9)

Provide an appropriate response.

10)

What amount will be in an account after 1.5 years if $4,000 is invested at 5% compounded

semiannually?

10)

Solve the problem.

11)

An ordinary annuity has a value of $1,333.85 at the end of 4 years when $150 is deposited

every 6 months into an account earning 6% compounded semiannually. How much

interest has been earned?

11)

12)

You can afford monthly deposits of $200 into an account that pays 8% compounded

monthly. How many months will it be until you have $15,000 to buy a car? (Round up to

the next higher month if not an integer.)

12)

Provide an appropriate response.

13)

An investment company pays 7% compounded quarterly. What is the effective rate?

(Compute the answer to two decimal places).

13)

Use an amortization table to solve the problem. Round to the nearest cent.

14)

You have purchased a new house and have a mortgage for $90,000 at 6% compounded

monthly. The loan is amortized over 20 years in equal monthly payments of $644.79. Find

the total amount paid in interest when the mortgage is paid off.

14)

Solve the problem. Round to the nearest cent as needed.

15)

You have decided to buy a new stereo system for $2,500 and agreed to pay in 30 equal

quarterly payments at 1.25% interest per quarter on the unpaid balance. How much are

your payments?

15)

Solve the problem.

16)

You deposit $130 each month into a savings account that pays 5.5% compounded monthly.

How much interest will you have earned after 8 years?

16)

Provide an appropriate response.

17)

A bank account starts with $1,000 in it. Interest is paid at 6% annual interest, compounded

monthly. Graph the exact function for the amount in the account over the first 12 months.

Use vertical scale [900, 1,200].

17)

Use an amortization table to solve the problem. Round to the nearest cent.

18)

A bank makes a home mortgage loan of $180,000 at 7.25% amortized in equal monthly

payments over 30 years. What is the total amount paid in interest when the mortgage is

paid off (round to the nearest dollar)?

18)

Solve the problem. Round to the nearest cent as needed.

19)

How many months will it take until an account will have $3,500 if $2,500 is invested now

at 5% compounded monthly?

19)

Provide an appropriate response.

20)

If an investor buys a 39–week T–bill with a maturity value of $25,000 for $23,543 what

annual interest rate (annual yield) will the investor earn? (Express your answer as a

percentage, correct to one decimal place.)

20)

Solve the problem.

21)

What is the future value of an ordinary annuity at the end of 3 years if $200 is deposited

each quarter into an account earning 6% compounded quarterly?

21)

Provide an appropriate response.

22)

An investor purchased 150 shares of a stock at $15.80 per share. The investor holds the

stock for 39 weeks and then sells the stock for $19.25 per share. Use the commission

schedule for this company given below to find the annual rate of interest earned by this

investor. Express your answer as a percentage, correct to one decimal place.

Principle Commission

Under $2500 $25 + 1.6% of principle

$2500 – $7500 $38 + 1.1% of principle

Over $7500 $105 + 0.5% of principle

22)

23)

If you pay $5,500 for a simple interest note that will be worth $6,000 in 21 months, what

annual simple interest rate will you earn? (Compute the answer to one decimal place.)

23)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use I = Prt for simple interest to find the indicated quantity.

24)

P = $22,660; r = 13%; 2.4 years. Find I.

24)

A)

$15,590.08

B)

$7069.92

C)

$29,729.92

D)

$2945.80

What is the annual percentage yield (APY) for money invested at the given annual rate? Round results to the nearest

hundredth of a percent.

25)

3.5% compounded continuously.

25)

A)

3.50%

B)

3.56%

C)

3.53%

D)

3.55%

Solve the problem. Round to the nearest cent as needed.

26)

Brandon’s savings account has a balance of $4069. After 4 years what will the amount of interest be

at 5% compounded quarterly?

26)

A)

$101.73

B)

$899.73

C)

$894.73

D)

$885.73

Find the compound amount for the deposit. Round to the nearest cent.

27)

$15,000 at 10% compounded semiannually for 10 years

27)

A)

$30.000.00

B)

$38,906.14

C)

$24,433.42

D)

$39,799.47

Use the formula A = P(1 +

rt) to find the indicated quantity.

28)

P = $7996; r = 6%; t = 10 months. Find A.

28)

A)

$399.80

B)

$6663.33

C)

$8475.76

D)

$8395.80

Solve the problem. Round dollar amounts to the nearest cent. Use 360 days.

29)

What is the purchase price of a 26–week T–bill with a maturity value of $1000 that earns an annual

interest rate of 5.25%?

29)

A)

$1025.58

B)

$25.58

C)

$974.42

D)

$1000

Solve the problem. Round to the nearest cent as needed.

30)

Cheraw Auto Repair believes that it will need new equipment in 10 years. The equipment will cost

$26,000. What lump sum should be invested today at 8% compounded semiannually, to yield

$26,000?

30)

A)

$17,637.61

B)

$21,097.18

C)

$11,866.06

D)

$17,462.98

Convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal

form.

31)

11.6% to decimal

31)

A)

0.116

B)

0.00116

C)

11.6

D)

116

Solve the problem.

32)

If $300,000 is to be saved over 25 years, how much should be deposited monthly if the investment

earns 8% interest compounded monthly?

32)

A)

$260.87

B)

$315.45

C)

$216.62

D)

$180.48

Use the formula A = P(1 +

rt) to find the indicated quantity.

33)

Allan borrowed $6300 from his father to buy a car. He repaid him after 9 months with interest of

7% per year. Find the total amount he repaid.

33)

A)

$6594.00

B)

$6630.75

C)

$6741.00

D)

$330.75

Solve the problem. Round to the nearest cent as needed.

34)

The monthly payments on a $73,000 loan at 13% annual interest are $807.38. How much of the first

monthly payment will go toward the principal?

34)

A)

$16.55

B)

$790.83

C)

$702.42

D)

$104.96

Solve the problem.

35)

At the end of every 3 months, Judy deposits $100 into an account that pays 6% compounded

quarterly. After 4 years, she puts the accumulated amount into a certificate of deposit paying 7.5%

compounded semiannually for 1 year. When this certificate matures, how much will Judy have

accumulated?

35)

A)

$1930.25

B)

$1823.20

C)

$2072.31

D)

$1920.96

Find the compound interest earned. Round to the nearest cent.

36)

$14,000 at 5% compounded annually for 3 years

36)

A)

$2206.75

B)

$2100.00

C)

$1435.00

D)

$701.50

Solve the problem. Round to the nearest cent as needed.

37)

The rabbit population in a forest area grows at the rate of 8% monthly. If there are 260 rabbits in

September, find how many rabbits (rounded to the nearest whole number) should be expected by

next September. Use y =260(2.7)0.08t

37)

A)

662

B)

674

C)

675

D)

688

Find i (the rate per period) and n (the number of periods) for the annuity.

38)

Semiannual deposits of $400 are made for 10 years into an annuity that pays 7% compounded

semiannually.

38)

A)

i = 0.035; n = 20

B)

i = 0.0175; n = 40

C)

i = 0.07; n = 10

D)

i = 0.35; n = 10

Solve the problem. Assume that the minimum payment on a credit card is the greater of $20 or 2% of the unpaid balance.

39)

Find the minimum payment on an unpaid balance of $890.94.

39)

A)

$20.00

B)

$22.82

C)

$17.82

D)

$178.19

Find the compound amount for the deposit. Round to the nearest cent.

40)

$1100 at 3% compounded quarterly for 2 years

40)

A)

$1166.00

B)

$1166.99

C)

$1116.56

D)

$1167.76

Use an amortization table to solve the problem. Round to the nearest cent.

41)

The monthly payments on a $73,000 loan at 13% annual interest are $807.38. How much of the first

monthly payment will go toward the principal?

41)

A)

$16.55

B)

$104.96

C)

$790.83

D)

$702.42

Find the payment necessary to amortize the loan.

42)

$11,500; 12% compounded monthly; 48 monthly payments

42)

A)

$298.02

B)

$1386.01

C)

$303.05

D)

$302.84

Find the monthly house payment necessary to amortize the following loan.

43)

In order to purchase a home, a family borrows $267,000 at 10.8% for 15 yr. What is their monthly

payment? Round the answer to the nearest cent.

43)

A)

$3001.27

B)

$19,108.39

C)

$2403.00

D)

$3394.52

Find the amount that will be accumulated in the account under the given conditions.

44)

The principal $15,400 is accumulated with simple interest of 16% for 5 years.

44)

A)

$15,892.80

B)

$12,320

C)

$27,720

D)

$20,212.50

Use I = Prt for simple interest to find the indicated quantity.

45)

P = $13,500; t = 4 months; I = $517.50. Find r.

45)

A)

11.7%

B)

7.7%

C)

11.5%

D)

3.8%

Solve the problem. Round to the nearest cent.

46)

Cara needs $9,000 in 8 years. What amount can she deposit at the end of each quarter at 8% interest

compounded quarterly so she will have her $9,000?

46)

A)

$203.50

B)

$846.13

C)

$212.37

D)

$195.18

Find i (the rate per period) and n (the number of periods) for the loan at the given annual rate.

47)

Annual payments of $378.80 are made for 8 years to repay a loan at 6.4% compounded annually.

47)

A)

i = 0.008; n = 8

B)

i = 0.064; n = 8

C)

i = 0.064; n = 16

D)

i = 0.00533; n = 12

Solve for the missing value. Round to four decimal places.

48)

n =33; i =0.05; PMT = $1; PV = ?

48)

A)

$23.9975

B)

$15.8027

C)

$16.0025

D)

$16.1929

Use the average daily balance method to compute the amount of interest that will be charged at the end of the billing

cycle. Use a 365–day year.

49)

Month: February (28 days)

Previous month’s balance: $1220

Interest rate: 20%

Date Transaction

February 3 made payment of $310

February 12 purchase of $325

February 21 purchase of $41

February 22 purchase of $68

49)

A)

$17.77

B)

$16.43

C)

$7.46

D)

$14.39

Convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal

form.

50)

0.05 to percent

50)

A)

0.05%

B)

50%

C)

0.0005%

D)

5%

Use I = Prt for simple interest to find the indicated quantity.

51)

P = $3000; t = 90 days; I = $105. Find r. (Use 360 days in a year.)

51)

A)

9.7%

B)

14.0%

C)

3.5%

D)

14.2%

Find the rate of interest required to achieve the conditions set forth.

52)

A = $32,000

P = $8,000

t = 20 years

compounded quarterly

52)

A)

5.5310%

B)

3.4959%

C)

3.5489%

D)

6.9919%

Solve the problem. Round to the nearest cent as needed.

53)

An actuary for a pension fund need to have $14.6 million grow to $22 million in 6 years. What

interest rate compounded annually does he need for this investment to growth as specified. Round

your answer to the nearest hundredth of a percent.

53)

A)

7%

B)

7.7%

C)

0.07%

D)

7.07%

Find the compound interest earned. Round to the nearest cent.

54)

$700 at 8% compounded semiannually for 4 years

54)

A)

$118.90

B)

$595.65

C)

$252.34

D)

$258.00

Solve the problem. Round to the nearest cent.

55)

Joe wants to start an SEP–IRA that will have $460,000 in it when he retires in 15 years. How much

should he invest semiannually in his IRA to do this if the interest is 15% compounded

semiannually?

55)

A)

$17,612.13

B)

$4790.74

C)

$44.35.77

D)

$4448.77

Solve the problem.

56)

How long will it take for $1400 to grow to $39,800 at an interest rate of 10.2% if the interest is

compounded continuously? Round the number of years to the nearest hundredth.

56)

A)

3.28 yr

B)

0.33 yr

C)

3281.76 yr

D)

32.82 yr

Find the rate of interest required to achieve the conditions set forth.

57)

If Jay bought a lot for $8,000 and sold it 15 years later for $24,000, what was her percentage rate of

return on this investment if it was compounded annually?

57)

A)

7.5990%

B)

3.7995%

C)

8.7104%

D)

9.6825%

Make the indicated conversion. Assume a 360–day year as needed.

58)

150 days to a simplified fraction of year

58)

A)

5

36

B)

15

365

C)

5

12

D)

15

12

Find i (the rate per period) and n (the number of periods) for the annuity.

59)

Monthly deposits of $1600 are made for 6 years into an annuity that pays 9% compounded

monthly.

59)

A)

i = 0.09; n = 72

B)

i = 0.75; n = 6

C)

i = 0.0075; n = 72

D)

i = 0.75; n = 12

Convert the given interest rate to decimal form if it is given as a percentage, and to a percentage if it is given in decimal

form.

60)

0.05% to decimal

60)

A)

0.0005

B)

0.05

C)

0.5

D)

5.0

Solve the problem. Round to the nearest cent as needed.

61)

The bacteria in a 9–liter container double every 4 minutes. After 54 minutes the container is full.

How long did it take to fill a quarter of the container?

61)

A)

46 min

B)

40.5 min

C)

13.5 min

D)

27 min

Solve the problem. Round dollar amounts to the nearest cent. Use 360 days.

62)

Polson Associates bought a new computer system. To pay for the system, they borrowed $41,950

from the bank at 8 3

4% interest for 130 days. Find the simple interest.

62)

A)

$1307.35

B)

$3670.63

C)

$1325.50

D)

$1315.31

Solve the problem. Round to the nearest cent as needed.

63)

Samantha’s savings account has a balance of $4643. After 25 years, what will the amount of interest

be at 6% compounded annually?

63)

A)

$15,275.16

B)

$2785.80

C)

$15,284.16

D)

$15,289.16