# FINANCIAL MATHEMATICS AUGUST 2021 PAST PAPER

MONDAY: 30 August 2021.        Time Allowed: 3 hours.

Answer ALL questions. Marks allocated to each question are shown at the end of the question. Show ALL your workings.

QUESTION ONE

1.           Outline four applications of financial forecasting.      (4 marks)

2.          Biashara Limited borrowed Sh.240,000 from Faidi bank at an interest rate of 3.5% compounded monthly. The loan is to be amortised using reducing balance method and be repaid in 12 equal monthly instalments payable at the end of each month.

Required:

Prepare a loan amortisation schedule for Biashara Limited.     (6 marks)

3.           Zaplon Limited has forecasted the following end of period prices of its shares:

Price per share (Sh.)                   Probability

24                                            0.08

29                                            0.14

35                                            0.22

38                                            0.13

48                                            0.43

The current price per share is Sh.35.

Required:

The expected return.    (3 marks)

The variance of the returns.   (3 marks)

The standard deviation.     (1 mark)

4.         An equipment which cost Sh.3,200,000 depreciates to a scrap value of Sh.400,000 in a period of ten years.

Depreciation on the equipment is on a reducing balance basis.

Required:

The implied rate of depreciation on the equipment.     (3 marks)

(Total: 20 marks)

QUESTION TWO

1.         Outline three advantages and three disadvantages of payback period as a method of project appraisal.  (6 marks)

2.        Highlight three differences between “correlation” and “regression”.      (3 marks)

3.          The following data relates to annual sales and profits of major supermarkets in East Africa:

Supermarket                        A                 B                 C                D                E                 F                 G                H

Sales (Sh.million)              1,130             809         1,280             552             689         1,135             915          1,055

Profits (Sh.million)            32.0          27.0           40.2           11.4            30.0           66.2           28.6           42.2

Required:

The regression equation of profit on sales.    (6 marks)

Predict profit for a similar company with sales of Sh.1,000 million.     (2 marks)

Comment on your analysis in  (ii) above.       (3 marks)

(Total: 20 marks)
QUESTION THREE

1.           A contractor has estimated that the weekly marginal mining cost in thousands of shillings per lorry per week is given by the following function:

y = —x + 15 + 100/x       ;        where x is the number of lorries.

Required:

The value of x  when y = 0.     (4 marks)

The weekly mining costs assuming the contractor currently operates 10 lorries.   (2 marks)

2.         In a certain manufacturing process, it is assumed that approximately 5% of the products are defective. A random sample of 20 items are selected from the output. If more than two defective items are discovered in the sample, the sample is rejected and vice versa.

Required:

Determine the proportion of the sample that can be rejected.   (4 marks)

Calculate the mean and variance of the sample.    (4 marks)

3.           The following table shows two sets of cash flows generated by two companies; A and B respectively over a period of eight years:

The interest rate of the cash flows is 12%.

Required:

Determine the company whose cash flow has a higher net present value (NPV).     (6 marks)

(Total: 20 marks)

QUESTION FOUR

1.

Required:

The joint profit function.     (4 marks)

The price and quantity of products X and Y that would maximise joint profit.    (6 marks)

The maximum joint profit.  (2 marks)

2.           The profits earned by 200 companies in Nyamindo county during the year ended 31 December 2020 are as follows:

Profit Sh. “millions”                Number of companies

40    — 60                                                         8

60    — 80                                                       16

80   — 100                                                     36

100 — 120                                                   60

120 — 140                                                    30

140 — 160                                                   20

160 — 180                                                    16

180 — 200                                                    14

200

Required:

Compute the 4th decile profit.       (4 marks)

Determine the 80th percentile profit.        (4 marks)

(Total: 20 marks)

QUESTION FIVE

1.           Explain the two conditions of a turning point as used in calculus.      (4 marks)

2.          Distinguish between “mutually exclusive events” and “conditional events” as used in probability.    (4 marks)

3.          The quantities and prices of three products consumed over the past four years in Tama county are provided in the table below:

Required:

Laspeyres and Paasche price indices for 2020 taking 2017 as a base year.   (6 marks)

Laspeyres and Paasche quantity indices for 2020 taking 2018 as a base year.     (6 marks)

(Total: 20 marks)

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