## TMA Solutions: BUS729 - Business Mathematics

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### TMA Solutions: BUS729 - Business Mathematics

1 The final value of a 7 year annuity-due with nominal annual interest rate 9% and monthly payments of \$100 ____________

11730.01

2 An ________due is an annuity whose payments are made at the beginning of each period.

annuity

3 The present value of a 5 year annuity with nominal annual interest rate 12% and monthly payments of \$100 is __________

4495.5

4 The__________ of an annuity entails concepts such as time value of money, interest rate, and future value.

valuation

5 __________are required at the end of each period.

Ordinary Annu ity

6 Write down a regular partition for [1, 8], n = 7. ________________

[1, 2, 3, 4, 5, 6, 7, 8]

7 ___________programming deals with the optimization (maximization or minimization) of a function of variables.

linear

8 ___________amount is also referred to as face amount.

par

9 The ___________ amount of a bond is the amount of principal that the bondholder will receive at maturity.

par

10 __________rate bonds have the advantage of being less volatile in price.

Floating

11 _________ coupon bonds do not make coupon payments during the life of the bond.

zero

12 The rate of interest that a bond pays to the bondholder is called the ___________.

coupon rate

13 ___________are a way for markets and participants to easily transfer the ownership of debt obligations from one party to another.

Debt instru ments

14 Suppose you invest #2000 at an annual interest rate of % 6. Find your balance at the end of 1 year if interest is compounded yearly __________

#2120

15 Interest that is computed on the previously accumulated interest as well as on the principal is called ________interest.

compound

16 William Pitt the Younger drafted a proposal to reform the Sinking Fund in __________.

1786

17 The sinking fund was first used in Great Britain in the _______ th century.

18

18 Cash Flow from financing activities includes _________ and buying back capital stock.

issuing

19 Cash Flow from investing activities includes purchasing and _______ long-term assets and marketable securities.

selling

20 ___________is preferred by most firms because is shows a reconciliation from reported net income to cash provided by operations.

indirect metho d

21 Empirical probability is often referred to as ____________ frequency.

relative

22 ___________is a concept that most people understand naturally since such words as 􀳦??chance,􀳦? 􀳦 􀳦??likelihood,􀳦?􀳦 􀳦??possibility􀳦?􀳦 and 􀳦??proportion are used as part of everyday speech.

Probability

23 A ___________ or joint event is an event that has two or more characteristics.

compound

24 Solve the inequalities: 3 􀳦?? 2X < 6. ___________

X 􀳦?􀳦 -3/2

25 Solve the inequalities: 2(X - 3) < 4. ___________

X < 5

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### Re: TMA Solutions: BUS729 - Business Mathematics

26 An _____________is simply a statement that two numbers are not equal.

inequality

27 Suppose f is a linear function with slope of 2 and f(4) = 8, find f(x)______________

f(x) = 2x

28 Solve for X and Y in the system of equations: 3X 􀳦?? 4Y = 13􀳦?􀳦􀳦?􀳦equ 1, 3Y + 2X = 3 􀳦? 􀳦􀳦?􀳦.equ 2. ____________

X = 3; Y = -1.

29 A ___________equation system is a set of equations with two or more unknown.

simultan eous

30 This symbol 􀳦? dates back to Leibniz and it is called ___________ sign.

integral

31 Let M be the set of the days of the week. The M is ____________

finite

32 Sets can be __________ or infinite.

finite

33 State in words and then write in tabular form C = {x}􀳦??x

C=􀳦 ?
34 State in words and then write in tabular form B = {x}􀳦??x-2=5}

hence B = {7}

35 State in words and then write in tabular form A = {x}􀳦??x ² = 4²}

A = {2, -2}

36 Elements are separated by commas and enclosed in _________

bracket

37 Let A consist of numbers 1,3,7, and 10, then we write ____________

A={1,3,7,10 }

38 __________case letters will usually represent the elements in our sets.

lower

39 Sets will usually be denoted by ________ letters.

capita l

40 A _______ is any well-defined list, collection or class of objects􀳦?􀳦.

set

41 Empirical probability is often referred to as ____________ frequency.

relative

42 ___________is a concept that most people understand naturally since such words as 􀳦??chance,􀳦? 􀳦 􀳦??likelihood,􀳦?􀳦 􀳦??possibility􀳦?􀳦 and 􀳦??proportion are used as part of everyday speech.

Probability

43 A ___________ or joint event is an event that has two or more characteristics.

compound

44 Solve the inequalities: 3 􀳦?? 2X < 6. ___________

X 􀳦?􀳦 -3/2

45 Solve the inequalities: 2(X - 3) < 4. ___________

X < 5

46 An _____________is simply a statement that two numbers are not equal.

inequality

47 Suppose f is a linear function with slope of 2 and f(4) = 8, find f(x)______________

f(x) = 2x

48 Solve for X and Y in the system of equations: 3X 􀳦?? 4Y = 13􀳦?􀳦􀳦?􀳦equ 1, 3Y + 2X = 3 􀳦? 􀳦􀳦?􀳦.equ 2. ____________

X = 3; Y = -1.

49 A ___________equation system is a set of equations with two or more unknown.

simultan eous

50 This symbol 􀳦? dates back to Leibniz and it is called ___________ sign.

integral

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51 Let M be the set of the days of the week. The M is ____________

finite

52 Sets can be __________ or infinite.

finite

53 State in words and then write in tabular form C = {x}􀳦??x

C=􀳦 ?

54 State in words and then write in tabular form B = {x}􀳦??x-2=5}

hence B = {7}

55 State in words and then write in tabular form A = {x}􀳦??x ² = 4²}

A = {2, -2}

56 Elements are separated by commas and enclosed in _________

bracket

57 Let A consist of numbers 1,3,7, and 10, then we write ____________

A={1,3,7,10 }

58 __________case letters will usually represent the elements in our sets.

lower

59 Sets will usually be denoted by ________ letters.

capita l

60 A _______ is any well-defined list, collection or class of objects􀳦?􀳦.

set

61 Interest that is computed on the principal alone is called __________ interest.

simple

62 ___________ is the fee charged for the privilege of borrowing money.

interest

63 Formula for sinking fund ______________

R = Ai / (1+i)n -1
64 A __________ fund is a fund established by an economic entity by setting aside revenue
over a period of time.

sink ing

65 ________ recommended "the Creation of a Fund.

Lord North

66 _______ is most often defined as operating cash flow minus capital expenditures.

Free cash flow

67 Cash Flow Indicator Ratios: Free Cash Flow/ _________

Operating Cash Flow Ratio

68 _____________indicates whether a company is able to generate sufficient positive cash flow to maintain and grow its operations

operational cash flow

69 ___________ of cash flow can be used for calculating other parameters that give information on a company's value and situation.

Measurement

70 ___________ is the movement of money into or out of a business, project of financial report.

cash flow

71 Variable annuities can grow tax deferred until ____________

withdraw n.

72 A ___________annuity is a contract between you and an issuer.

variable

73 There are _________ basic types of fixed annuities

two

74 ___________ are invested primarily in government securities and high-grade corporate bonds.

Fixed annuities

75 A ___________ is an annuity for which the payments continue forever.

perpetuity

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76 Annuities are primarily used as a means of securing a steady _________ for an individual during their retirement years.

cash flow

77 There are ______types of annuities and annuities due.

two

78 _________are essentially a series or fixed payments required from you or paid to you at a specified frequency over the course of a fixed time period.

annuities

79 A function f of A onto B is called a _________ function if the same element of bƐB is assigned to every element in A.

constant

80 Real number can be represented by a 􀳦??__________decimal􀳦?􀳦.

non-terminating

81 The natural numbers are the ________ integers.

positive

82 The ______numbers are those real numbers.

rational

83 The set of real numbers and its properties is called the __________.

real number system

84 The family of all the subsets of any set S is called the _______ set of S.

power

85 If every element in a set A is also a member of a set B, then A is called _______of B.

subset

86 Let B = {x | x²= 4, x is odd}, Then _____ is the empty set.

B

87 _________ is a set contains no elements.

null set

88 Let E={x | x²􀳦??3x = -2}, F={2,1} and G ={1,2,2, 1}. Then ___________

E= F= G

89 Let A = {1, 2, 3, 4} and B= {3, 1, 4, 2}. Then ___________

A = B,

0 Let N = {0,2,4,6,8........}.Then N is __________

infini te

91 State in words and then write in tabular form C = {x}􀳦??x

C=􀳦 ?

92 The natural numbers are the ________ integers.

positive

93 If every element in a set A is also a member of a set B, then A is called _______of B.

subset

94 Elements are separated by commas and enclosed in _________

bracket

95 A _______ is any well-defined list, collection or class of objects􀳦?􀳦.

set

96 ______theorem is a formula which can be thought of as 􀳦??reversing􀳦?􀳦 conditional probability.

Bayes

97 The _______ Probability of an event is its simple probability of occurrence, given the sample space

margi nal

98 A_________ probability implies the probability of joint events. Joint probabilities can be
conveniently analysed with the aid of joint probability tables.

joint

99 Assume there is a drug store with 10 antibiotic capsules of which 6 capsules are effective and 4 are defective.What is the probability of purchasing the effective capsules from the drug store? _________

25.2

100 __________ events are said to be mutually exclusive events if they cannot occur at the same time.

two

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1 There are two strategies of drawing the number line. It can be drawn horizontally or ________-.

Vertically

2 The positive numbers are usually called _________ integers.

Positive

3 _________ is a whole numbers that do not have any form of fraction associated with it.

Integer

4 When zero is included to the set of natural numbers we have what is called ________ numbers.

Whole

5 Zero was not a natural number so there were problems that became unresolved such as 2-2, 3-3, and

9 minus 9

6 The discovery of zero in _________ AD help resolved the problem in numbers.

600

7 The most common conversion is usually from base __________ to other bases

Ten

8 ___________ numbers can be converted from one base to another

9 Cubic numbers are numbers that are ___________ power of natural numbers

Third

10 __________ are natural numbers with no factor other than, unity or itself

Prime Numb ers

11 The indirect methods of prsenting cash flows become preferable because

it reconciliation from reported net inco me to cash provided by operations

12 The sinking fund was first used in Great Britain in the 18th century to reduce

national debts

13 A company wishes to spend #40000 for new equipment and decides to set up a sinking fund to accumute this money over a 3year period. If payments are to be made to the fund quartely with interest compounded quartely at an annual rate of 5%, how large should the payments?

3110.42 Naira

14 Which one is true about the Zero coupon bond?

do not make coupon payments during the life of the bond.

15 One of the assumptions of linear programming is the

16 The followings are the limitations of L. P except

Linear programming deals with prob lems that have multiple objectives

17 Solve the differential equation dx/dy - 4x3

X4C

18 Evaluate dy/dx 􀳦?? 2X +3

X2 + 3X + c

19 Evaluate 􀳦?􀳦30(x-1) (x-2) dx

3

20 The L.P is more applicable to the following except

Manpower developme nt problems

21 Linear programming basically deals

Optimazation of a function of variable known as objective function

22 Suppose you invest #2000 at an annual interest rate of % 6. Find your balance at the end of 1 year if interest is compounded semiannually

2120 .8

23 The final value of a 7 year annuity-due with nominal annual interest rate 9% and monthly payments of 100 Naira

11,730.01 Naira

24 What is the equivalence of 500 naira, if the amount is borrowed for 10years and if the interest is 15%

2023 Naira

25 The followings are the types of Cash flows except

Promotional cash flows

26 When payment occurs at the end of each period is called

Ordinary ann uity.

27 The following explain annuity

series of equal payments

28 The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is ___________

1111101010

29 The complement of the set B is _____________

U 􀳦?? B

30 Number of subsets of a set of order three is

8

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