COURSE WARE FOR ACC/FIN 226
MATHEMATICS FOR ACCOUNTING AND FINANCE
DEPARTMENT OF ACCOUNTING AND FINANCE,
FACULTY OF BUSINESS AND SOCIAL SCIENCES,
UNIVERSITY OF ILORIN
Course code: ACC 226
Course Title: Mathematics for Accounting and Finance
(3 Credit – Compulsory) 45 Hours (3 Hours per week)
Lecturer: DR AJAYI Michael Adebayo
PhD. Accounting and Finance,
M.Sc. Management Science (Unilorin),
Masters in Business Administration (Unilorin),
BSc. Banking and Finance (UNAD)

Email address: adeajayi4jesus@yahoo.com
maajayo@unilorin.edu.ng

Office Location: Room 8, Ground Floor, Adekanola Building,
Department of Accounting and Finance.

Consultation Hours: Monday and Wednesday 12noon to 1:00 PM
COURSE CONTENT

Algebraic and transcedental functions

Differential calculus: Limits and continuity. Derivation from first principles.

Total differential-application to marginal analysis, cost functions, indifference curves etc.

Maximisation and minimization.

Partial differentiation with application to marginal analysis and comparative statistics.

Integral calculus. Integration with application to marginal/total functions.

Producer and consumer surplus

Exponential and logarithmic functions.

Differential equators

Permutation and Combination

Simple sequence and series – finite and infinite

Convergent and divergent series
COURSE DESCRIPTION
Differential and integral calculus involves the establishment of turning points – minimum or maximum. The course
explains how cost is minimized by economic units and how these units maximizes revenue, hence, profit – which is
the main reason of going into business.
Permutation and Combination also details out how decision is made when faced the problem of arranging the
decision subject or selecting among these based on a specified rule.
COURSE JUSTIFICATION
This course will provide the students with the fundamentals of business mathematics. It basically contains the use of
mathematical techniques in solving the day-to-day problems that can be encountered in business. It models costs
revenue into functions which are used in making informed decision in business. It will also give the students the
required background that will assist them in subsequent courses during their degree programme, majorly financial
management.
COURSE OBJECTIVE
Students should be able to:

Understand the concept of derivatives

Differentiate various functions such as polynomial, product, quotient, function of function, implicit function,
exponential and logarithmic function.

Obtain second order derivative

Apply the principle of derivation to solve economic and business problems such as finding marginal,
elasticity, maximum and minimum value.

Understand the concept of simple partial differentiation of first order only.

Apply the concept of sequence and series in determining future values and point estimates of specified
decision variables
COURSE REQUIREMENT
This is a compulsory course for all accounting and finance students at 200 level. The students is expected to
participate actively in the class discussion and to have a minimum of 75% attendance to qualify for the final
examination. It is essential that individual student must do their assignments as appropriate and any student not
performing to expectation will be dropped from the course after examination where he/she may score a failed mark.
Method of Grading
No Item
Score%
1
Attendance
10
2
Class Test
20
3
Comprehensive Final Examination
70
Total
100
COURSE DELIVERY STRATEGY
The course objectives will be achieved through the use of traditional face to face teaching and group discussions/
presentations. Lecture notes and course materials will also be provided during lectures. The students will be divided
into groups and each group will defend their project work at the end of the semester through seminar presentations.
In class, quizzes (which may be impromptu) in conjunction with group works and final examination will be used to
determine students’ final grades.
The delivery strategies will also be supported through tutorial session’s review of study at the end of the semester.
Students will be encouraged and required t read around the topics and follow current issues in the business world.
Web interactions will be employed by requesting each student to have yahoo w-mail address to participate in the
yahoo discussion group that will be created for the course. Additional materials and links will be provided on the
board.
LECTURES
This course will be guided by the following course work schedule.
Week 1
In this class, students will learn:
Definition of a function
Solving linear and quadratic equation
Solving linear equations simultaneously
Solving for one linear and one quadratic equations simultaneously
Study Questions

What is a function?

What is the value of X in the following linear equations:
1. X – 6 = 24
2. 2(X + 4) – 1 = 10

Find the value of X and Y in the following equations by solving simultaneously:
1. Y = 2X – 8
5Y – 4X = 20
2. If it costs five hundred naira to buy forty blue pens and five green pens; and one thousand naira to buy
twenty blue pens and fifty green pens, what is the unit cost of the pens?

What is the value of Y and X that will satisfy the equations:
Y=X–1
Y = X2 +6X – 7
ASSIGNMENT

What is the value of X in the following linear equations:
1. 4X – 6 = 46
2. 5(X + 4) – 1 = 244

Find the value of X and Y in the following equations by solving simultaneously:
Y = 4X – 2
5Y – 4X = 38

If it costs 5,000 naira to buy 100 note books and 50 drawing books; and 1000 naira to buy 20 note books and
10 drawing books, what will be the cost of 25 note books and 4 drawing books?

What is the value of Y and X that will satisfy the equations:
Y = 2X – 1
Y = X2 +5X – 5
References
Berenson, M. L. and David M. L., (2006) Basic Business Statistics: Concepts and Applications, 8th edition (Upper
Saddle River, NJ: Prentice Hall).
David F. G., Patrick W. S., Philip C. F., and Kent D. S. (2008) Business Statistics: A Decision- Making Approach.
Seventh Edition.
Week 2
In this class, students will learn:

The relationship between cost function; revenue function and profit function

The relationship between the demand (price) function and cost function
Study Questions

A manufacturer knows that if x (hundred) products are demanded in a particular week: (i) the total cost
function(N’000) is 14 + 3x, and (ii) the total revenue function (N’000) is 19x -2x2
a) Derive the (total) profit function
b) Find the profit break-even points
c) Calculate the level of demand that maximizes profit (i.e the maximum profit point) and the amount of
profit obtained.

The variable costs associated with a certain process are N0.65 per item. The fixed costs per day have been
calculated as N250 with special costs estimated as N0.02x2, where x is the size of the production run (i.e
number of items produced).
a) Derive a function to describe cost per item for a day’s production.
b) Calculate the size of the daily run that will minimize cost per item.
c) Find the cost of a day’s production for a run that minimizes cost per item.
Assignment
Given that the price of an item is N3.50 when 250 items are demanded, but when only 50 are demanded, the price
rises to N5.50 per item, identify the linear demand function and calculate the price per item at a demand level of
115.
References
Berenson, M. L. and David M. L., (2006) Basic Business Statistics: Concepts and Applications, 8th edition (Upper
Saddle River, NJ: Prentice Hall).
Bowerman, B. L., and Richard T. O. Connell, (1993) Forecasting and Time Series; an Applied Approach, 3rd edition
(North Scituate, MA: Duxbury Press).
Johnson, R. A., and Dean W. W., (1997) Business Statistics: Decision Making with Data (New York: Wiley).
Week 3
In this class, students will learn:

Differentiation from first principle.

Obtaining the first order derivative of an equation.

Establishing the turning point of an equation

Establishing the nature of the turning point by obtaining the second order derivative
Study Questions


Differentiate the following using the first principle:
a. Y =
b. Y = 1/x
Find the value of
for the following functions:
a. y = 2
b. y = 4x
c. y =
d. y =

+
–4
Determine the nature of the turning point for the following:
1. P = 200q – 2q2 -2000
2. R = 500q – 2q2
Assignment


Differentiate the following using the first principle:
a. Y = 2 + 4
b. Y = (1/x)2
Find the value of
for the following functions:
a. y = 5
b. y = 100x
c. y =
+ 3x3 - 40x2 + 4
d. y =

+ 46x2 +4
Determine the nature of the turning point for the following:
a. P = 2q2 - 200q +2000
b. R = 2q2 + 500q
References
LUCEY T. (2000) Quantitative Analyses; Fifth Edition with Letts Education. London.
Willis, R. E., (1987) A Giude to Forecasting for Planners (Engle wood Cliffis, NJ: Prentice Hall)
Wonnacott, T. H., and R. J. Wonnacott, (1979) Econometrics, 2nd edition (New York: John Wiley & Sons).
Week 4
In this class, the students will learn:

Application of differential calculus to business
Study Questions
A manufacturer of a new patented product has found that he can sell 70 units a week direct to the customer if the
price is N48. In error, the price was recently advertised at N78 and, as a result, only 40 units were sold in a week. The
manufacturers fixed costs of production are N1,710 a week and variable costs are N9 per unit. You are required:
a. To show the equation of the demand function linking price (P) to quantity demanded (X), assuming it to be a
straight line, is P = 118 – X;
b. To find where the manufacturer breaks even;
c. To recommend a unit price which would maximise profit, and to find the quantity demanded and profit
generated at that price;
d. Assuming a sudden change in trading conditions resulting in a 20% reduction in demand at all price levels, to
find the equation of the new demand function and to recommend how the manufacturer should respond.
Assignment
At a selling price of N3.80 per unit the expected sales of particular product would be 10,200, but would fall to 8,400
if the selling price was N4.70. The total cost function (in N) for the product is 15,000 + 1.8x, where x is the number of
units.
a. Derive the demand function, assuming it is linear.
b. Derive an expression for total profit.
c. Calculate the maximum profit and the level of sales which achieves it.
d. What price is charged per unit at the maximum profit point?
References
LUCEY T. (2000) Quantitative Analyses; Fifth Edition with Letts Education. London.
Willis, R. E., (1987) A Giude to Forecasting for Planners (Engle wood Cliffis, NJ: Prentice Hall)
Wonnacott, T. H., and R. J. Wonnacott, (1979) Econometrics, 2nd edition (New York: John Wiley & Sons).
Week 5
In this class, students will learn:
Partial differentiation with application to marginal analysis and comparative statistics
References
LUCEY T. (2000) Quantitative Analyses; Fifth Edition with Letts Education. London.
Willis, R. E., (1987) A Giude to Forecasting for Planners (Engle wood Cliffis, NJ: Prentice Hall)
Wonnacott, T. H., and R. J. Wonnacott, (1979) Econometrics, 2nd edition (New York: John Wiley & Sons).
Week 6
In this class, the students will learn:

The basics of integral calculus

Integration as the opposite of differentiation

Application of integration to marginal/total functions
Study Questions
Solve the following
1.
2.
3. If
and y =12 when x =0, find y in terms of x
Assignment
1. The total revenue obtained (in N’000) from selling x hundred items in a particular day is given by R, which is a
function of variable x.
Given that
:
a. Determine the total revenue function R;
b. Find the number of items sold in one day that will maximize the total revenue and evaluate this total
revenue.
2. How many units of a product (x) should be produced to minimize the total cost function of:
a. y =
- 640x + 400
b. y =
+
–x+1
References
David F. G., Patrick W. S., Philip C. F., and Kent D. S. (2008) Business Statistics: A Decision- Making Approach.
Seventh Edition.
Johnson, R. A., and Dean W. W., (1997) Business Statistics: Decision Making with Data (New York: Wiley).
MURRAY R. S. and LARRY J. S. (2008) Theory and Problems Of Statistics; forth edition Schaum’s Outline.
Siegel, A. F., (2003) Practical Business Statistics, 5th edition (Burr Ridgr, IL: Irwin).
Week 7
In this class, students will learn:
Producer and consumer surplus and its application to business
The graphical representation between the quantities demanded of a good and the price of the good
The concept of equilibrium point
Study Questions
What does producer surplus measure?
What does consumer surplus measure?
The demand and supply equations are given by D(p) = 60 – q2/10 and S(q) = 30 + q2/5. Find the producers’ surplus at
the equilibrium price.
Assignment
The demand and supply equations are given by D(p) = 60 – q2/10 and S(q) = 30 + q2/5. Find the consumers’ surplus
at the equilibrium price.
References
Bowerman, B. L., and Richard T. O. Connell, (1993) Forecasting and Time Series; an Applied Approach, 3rd edition
(North Scituate, MA: Duxbury Press).
David F. G., Patrick W. S., Philip C. F., and Kent D. S. (2008) Business Statistics: A Decision- Making Approach.
Seventh Edition.
MURRAY R. S. and LARRY J. S. (2008) Theory and Problems Of Statistics; forth edition Schaum’s Outline.
Willis, R. E., (1987) A Giude to Forecasting for Planners (Engle wood Cliffis, NJ: Prentice Hall)
Week 8
In this class, students will learn:

What exponential and logarithmic functions are;

How to perform simple operations with exponential and logarithmic functions
References
Bowerman, B. L., and Richard T. O. Connell, (1993) Forecasting and Time Series; an Applied Approach, 3rd edition
(North Scituate, MA: Duxbury Press).
David F. G., Patrick W. S., Philip C. F., and Kent D. S. (2008) Business Statistics: A Decision- Making Approach.
Seventh Edition.
Week 9
In this class, students will learn:
What differential equators are
How to identify first order and second order differential equators
How to find the general and specific solutions of differential equations.
Study Questions
Find the general solution for the differential equation dy + 7xdx = 0
Find the particular solution given that y(0) =3
Find the particular solution of y’ =5 given that when x = 0, y = 2.
Find the particular solution of y’’’ = 0 given that: y(0) = 3, y’(1) = 4, y’’(2) = 6
Assignment
Find the general solution of the second order DE y’’ + a2y = 0
Find the general solution of the second order DE y’’ – 3y’ + 2y = 0
References
Berenson, M. L. and David M. L., (2006) Basic Business Statistics: Concepts and Applications, 8th edition (Upper
Saddle River, NJ: Prentice Hall).
Bowerman, B. L., and Richard T. O. Connell, (1993) Forecasting and Time Series; an Applied Approach, 3rd edition
(North Scituate, MA: Duxbury Press).
MURRAY R. S. and LARRY J. S. (2008) Theory and Problems Of Statistics; forth edition Schaum’s Outline.
LUCEY T. (2000) Quantitative Analyses; Fifth Edition with Letts Education. London.
Week 10
In this class, students will learn:

Permutation and its application to business

The concept of facotrial

Ways of arranging groups of items.
Study Questions
Solve the following:
1.
4
P2
2.
7
P3
3. How many ways are there for arranging 3 different jobs between 5 men, where any man can do only one
job?
4. What is the probability that man A will be doing job 1 in question ‘3’ above?
Assignment
1. How many ways can a twelve-man committee sit round a table to make operational policy for their
company?
2. How many ways can the letters of the word ‘MATHEMATICS’ be arranged?
References
Bowerman, B. L., and Richard T. O. Connell, (1993) Forecasting and Time Series; an Applied Approach, 3rd edition
(North Scituate, MA: Duxbury Press).
David F. G., Patrick W. S., Philip C. F., and Kent D. S. (2008) Business Statistics: A Decision- Making Approach.
Seventh Edition.
MURRAY R. S. and LARRY J. S. (2008) Theory and Problems Of Statistics; forth edition Schaum’s Outline.
LUCEY T. (2000) Quantitative Analyses; Fifth Edition with Letts Education. London.
Week 11
In this class, students will learn:
Combination and its application to business
References
David F. G., Patrick W. S., Philip C. F., and Kent D. S. (2008) Business Statistics: A Decision- Making Approach.
Seventh Edition.
MURRAY R. S. and LARRY J. S. (2008) Theory and Problems Of Statistics; forth edition Schaum’s Outline.
Willis, R. E., (1987) A Giude to Forecasting for Planners (Engle wood Cliffis, NJ: Prentice Hall)
Wonnacott, T. H., and R. J. Wonnacott, (1979) Econometrics, 2nd edition (New York: John Wiley & Sons).
Week 12
In this class, students will be introduced to the basics of Simple sequence and series and learn:
The difference between a sequence and a series
The fundamentals of Arithmetic Progression and Geometric Progression
Calculating the nth term; the sum of the first nth term and the sum to infinity of Arithmetic Progression and
Geometric Progression
Study Questions
For the AP: 2, 5, 8,.................., calculate:
a. The sixth term;
b. Sum of the first twenty terms;
c. The sum to infinity.
For the GP: 2, 4, 8, .............., calculate:
a. The sixth term;
b. Sum of the first twenty terms;
c. The sum to infinity.
Assignment
If a-1, b-1, c-1, d-1 is an Arithmetic Progression, show that:
a. b = 2ac/(a + c);
b. b = cd/(2d – c)
References
Berenson, M. L. and David M. L., (2006) Basic Business Statistics: Concepts and Applications, 8th edition (Upper
Saddle River, NJ: Prentice Hall).
David F. G., Patrick W. S., Philip C. F., and Kent D. S. (2008) Business Statistics: A Decision- Making Approach.
Seventh Edition.
Johnson, R. A., and Dean W. W., (1997) Business Statistics: Decision Making with Data (New York: Wiley).
Siegel, A. F., (2003) Practical Business Statistics, 5th edition (Burr Ridgr, IL: Irwin).
Week 13
In this class, students will learn:
The application of Arithmetic Progression (AP) to business
Study Questions
A company buys a computer for N1,250,000 and houses it in a specially constructed suite at a cost of N200,000.
a. If the computer depreciates at 25% (straight line) and the suite appreciates at 5% (simple), what is the book
value of the suite and computer after 5 years?
b. Taking computer and suite together and using the straight line method, what if the overall depreciation
rate?
Assignment
A company’s capital reserve at the end of 2009 financial year is N400,000. If the firm transfers N20,000 each year
from its profit for the year to capital reserve, how long will it take the company to make a bonus issue of N450,000
out of the reserve to existing ordinary shareholders and leave N50,000 balance after the issue.
References
Bowerman, B. L., and Richard T. O. Connell, (1993) Forecasting and Time Series; an Applied Approach, 3rd edition
(North Scituate, MA: Duxbury Press).
Johnson, R. A., and Dean W. W., (1997) Business Statistics: Decision Making with Data (New York: Wiley).
Siegel, A. F., (2003) Practical Business Statistics, 5th edition (Burr Ridgr, IL: Irwin).
LUCEY T. (2000) Quantitative Analyses; Fifth Edition with Letts Education. London. Wonnacott, T. H., and R. J.
Wonnacott, (1979) Econometrics, 2nd edition (New York: John Wiley & Sons).
Week 14
In this class, students will learn:
The application of Geometric Progression to Business
A company buys a computer for N1,250,000 and houses it in a specially constructed suite at a cost of N200,000.
a. If the computer depreciates at 25% (reducing balance) and the suite appreciates at 5% (compound), what is
the book value of the suite and computer after 5 years?
b. Taking computer and suite together and using the reducing balance method, what if the overall depreciation
rate?
Assignment
A company’s capital reserve at the end of 2009 financial year is N40,000. If the firm transfers 50%each year from its
profit for the year to capital reserve, how long will it take the company to make a bonus issue of N450,000 out of the
reserve to existing ordinary shareholders and leave N50,000 balance after the issue? What amount is transferred
from profit after tax annually to the reserve?
References
Berenson, M. L. and David M. L., (2006) Basic Business Statistics: Concepts and Applications, 8th edition (Upper
Saddle River, NJ: Prentice Hall).
Bowerman, B. L., and Richard T. O. Connell, (1993) Forecasting and Time Series; an Applied Approach, 3rd edition
(North Scituate, MA: Duxbury Press).
David F. G., Patrick W. S., Philip C. F., and Kent D. S. (2008) Business Statistics: A Decision- Making Approach.
Seventh Edition.
MURRAY R. S. and LARRY J. S. (2008) Theory and Problems Of Statistics; forth edition Schaum’s Outline.
LUCEY T. (2000) Quantitative Analyses; Fifth Edition with Letts Education. London.
Week 15
This class will be a revision c lass for what has been taught from WEEK 1 to WEEK 14
Study Questions
1. Find the value of
for the following functions:
4. y = 2
5. y = 4x
6. y =
7. y =
+
–4
2. Differentiate the following using the first principle:
8. Y =
9. Y = 1/x
3. Find the value of
a. Y = 8
b. Y = 8
-
for the following functions:
+4
+8
4. How many units of a product (x) should be produced to minimize the total cost function of:
c. y =
- 640x + 400
d. y =
+
–x+1
5. Given that the cost (y) in Question 4 is in thousands of Naira, Calculate the minimum cost. The total cost
function for a producer is given as C = – 4 while the price function is given as P = – 4
6. How many ways can a six-man committee sit round a table to make operational policy for their company?
7. How many ways can the letters of the word ‘MAXIMUM’ be arranged?
8. In how many ways can a 5 man committee be constituted out 4 men and 6 women such that the committee
contains:
a. More men than women;
b. More women than men;
c. Only one man;
d. No man at all;
e. Only one woman.
What is the probability of ‘a’ to ‘e’ above.