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Cfm 001 Financial Mathematics Question Paper

Cfm 001 Financial Mathematics

Course:Diploma In Business Management

Institution: Kca University question papers

Exam Year:2014

UNIVERSITY EXAMINATIONS: 2013/2014
STAGE I ORDINARY EXAMINATION FOR THE CERTIFICATE IN
BUSINESS MANAGEMENT
CFM 001 FINANCIAL MATHEMATICS
DATE: AUGUST 2014
TIME: 1 1/2 Hours
INSTRUCTION: Answer any THREE questions
QUESTION ONE: (20 MARKS)
The Table below presents the number of policies signed up by the Sales Team of Realval
Insurance Agency
26 20 22 16 25 21 19 15
19 15 25 15 18 20 39 32
12 14 19 21 15 25 18 23
8 11 18 23 22 16 17 31
45 14 31 24 14 30 15 22
Required:
(a)
Present the above data in a grouped frequency table. (hint: find the class size).
(4 Marks)
(b) Prepare a histogram presenting the above distribution.
(c)
(4 Marks)
Find:
i. The Median for the Sales (3 Marks)
ii. The Mode Sales (3 Marks)
iii. The average by the sales team (3 Marks)
iv. The Variance and Standard Deviation for the sales. (3 Marks)
1
QUESTION TWO: (20 MARKS)
(a)
You have been proposed two projects with the following predictions
Project A
Assumptions (states of nature)
Net Present Value Sh`000''
Probability
Pessimistic 200 0.6
Moderately successful 400 0.3
Optimistic 600 0.1
Project B
Assumptions (states of nature)
Net Present Value Sh`000''
Probability
Pessimistic 300 0.5
Moderately successful 400 0.2
Optimistic 500 0.3
Required:
i. (4 Marks)
ii.
(b)
Find the Expected value of each project Compare the risks of the two projects using standard deviation (4 Marks)
The demand of flash disks at Computer Africa is 30 units when the price is sh.100 and 48
units when the demand is sh. 70.
Required:
i. (4 Marks)
ii.
(c)
Derive a linear demand function for the product. Compute the price that will respond to a demand of 16 units. (4 Marks)
Outline the applications of time series in financial forecasting.
(4 Marks)
QUESTION THREE: (20 MARKS)
(a)
The marginal revenue of a company is given by the expression MR= 400-8q while the
marginal cost is given by the expression MC=2Q-100. Fixed costs amount to sh. 8000.
“q” represents the number of units produced and sold by the company.
Required:
i. Derive the total revenue, cost and profit functions. (6 Marks)
ii. Determine the maximum profits. (4 Marks)
2
(b)
Kiriba invests Shs. 100, 000 in two investment funds. Investment A attracts a simple
interest of 10% per annum wile Investment B attracts a compound interest of 8 % per
annum.
Required:
Find the value of the two funds in three years
(c)
(6 Marks)
Explain any two components of a time series (4 Marks)
QUESTION FOUR: (20 MARKS)
(a)
You are the investment Manager of Cetrumia Investments. You are planning to invest a
total of Limited Ksh.1, 400,000 into a fund attracting a compound interest of 12%.
Calculate the amount in the account in two years if it is compounded:
i. Annually. (3 Marks)
ii. Semi-annually. (3 Marks)
iii. Quarterly. (3 Marks)
iv. Monthly. (3 Marks)
v. Weekly. (4 Marks)
vi. Daily. (4 Marks)
QUESTION FIVE: (20 MARKS)
(a)
The following data represents the 91 day- treasury bill rates for the years 2008 and 2009.
Month
Treasury Bill Rates (%)
2012 2013
January 3.2 3.0
February 3.3 3.3
March 2.7 3.6
April 2.8 4.0
May 2.6 4.0
June 2.8 3.9
July 3.0 4.0
3
August 3.2 4.2
September 3.2 4.2
October 3.2 3.6
November 3.1 2.8
December 2.9 2.7
Required:
i. The arithmetic mean of the treasury bill rates for each year. (4 Marks)
ii. The standard of the treasury bill rates for each year. (4 Marks)
iii. The coefficient of variation of the treasury bill rates for each year. (4 Marks)
(b) Differentiate between the Laspeyre’s Price index and Paasche’s Price index.
(c) Distinguish between the compound interest of a lumpsum and the compound interest of
an annuity.
(4 Marks)
(4 Marks)
4

Cfm 001 Financial Mathematics Question Paper

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