CIMA - C3 Fundamentals Of Business Mathematics
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340 Question bank
(d) The company is liable to replace any battery which lasts for less than 40 hours. The company wishes
to reduce the percentage of defective batteries from the current level of 4% to 2%.
(i) Use normal tables to find the value 'b' such that P(z < b) = 2%.
(ii) The company can use a chemical procedure which changes the values of the mean and
standard deviation. If the standard deviation is set at 35 hours, find the mean lifetime which
will reduce the percentage of defectives to 2%.
64 How much will an investor have after eight years if he invests $2,000 at 12% per annum simple interest?
A $1,920
B $3,680
C $3,920
D $4,952
65 In four years, an investment of $900 has grown to $1,548. What has been the monthly rate of simple
interest?
A 1.1%
B 1.5%
C 15%
D 18%
66 A one-year investment yields a return of 20%. The cash returned from the investment, including principal
and interest is $3,000. The interest is
A $300
B $400
C $500
D $600
67 It is estimated that a particular cost will decline by 8% per annum on a compound basis.
If the cost is now $12,000, by the end of year 3 the cost will be approximately
A $8,597
B $9,120
C $9,344
D $10,157
68 House prices rise at 3% per calendar month. The annual rate of increase correct to one decimal place is
A 42.6%
B 36.0%
C 14.26%
D 12.36%
69 (a) The effective annual rate of interest of 15% nominal per annum compounded quarterly is
%
(b) The effective annual rate of interest of 24% nominal per annum compounded monthly is
%
Question bank 341
70 The treasurer of Hound Camping Co needed to invest some surplus cash. He decided to make the following
investments. Calculate the interest earned on each of the following investments (correct to the nearest $).
(a) $8,000 was placed in a bank deposit account for three years. The expected annual rate of interest is
11%, calculated yearly.
(b) $15,000 was placed in a savings account for five years, with interest added yearly at 14%.
(c) $6,000 was placed in an account for four years where the annual interest rate is expected to be 10%
for the first two years and 15% in years 3 and 4, with interest added at the end of each year.
The treasurer is also considering three further investments A, B and C. In each case calculate the effective
annual rate of interest to 2 decimal places.
(d) Investment A would last for three years, and pay interest at a nominal rate of 10.5%. Compound
interest would be added every half year.
(e) Investment B would last for five years, with a nominal interest rate of 12%, payable monthly.
(f) Investment C would last for four years, with a nominal interest rate of 12%, payable quarterly.
71 A firm has arranged a ten-year lease, at an annual rent of $12,000. The first rental payment has to be paid
immediately, and the others are to be paid at the end of each year.
What is the present value of the lease at 12%?
A $63,936
B $67,800
C $75,936
D $79,800
72 A mortgage of $60,000 is to be repaid by 15 equal year-end payments. If interest is charged at 9% the value
of the annual payment (using tables) correct to the nearest $10 is
A $2,050
B $4,000
C $6,830
D $7,440
342 Question bank
73 The NPV of an investment is $460 when the cost of capital is 10% and $320 when it is 24%. Estimate the
internal rate of return to two decimal places.
A 17.00%
B 18.20%
C 56.00%
D It is not possible to estimate the IRR unless one of the NPVs is negative
74 Over a period of 12 months, the present value of the payments made on a credit card is $21,000 at a
discount rate of 3% per month. What is the equivalent constant monthly amount, to the nearest $?
A $1,750
B $2,110
C $8,743
D $14,721
75 Which of the following mutually exclusive projects would you advise your client to undertake if only one
could be undertaken, given
only the following information.
IRR NPV
% $
Project A 15.6 1,600
Project B 16.7 1,400
Project C 17.6 1,200
Project D 18.5 1,000
A Project A
B Project B
C Project C
D Project D
76 Daisy Co is considering whether to make an investment costing $28,000 which would earn $8,000 cash per
annum for five years. The company expects to make a return of at least 11% per annum.
Complete the following table and state whether the project is viable or not.
Year Cash flow Discount factor Present value
$ 11% $
0
1
2
3
4
5
NPV
Project viable Yes
No
Question bank 343
77 Daisy Hoof Co is considering a project to purchase some equipment which would generate the following
cash flows.
Year Cash flow
$
0 (50,000)
1 18,000
2 25,000
3 15,000
4 10,000
The estimated trade-in value of the equipment, which is $2,000, has not been included in the cash flows
above.
The company has a cost of capital of 16%.
Required:
(a) Complete the following table by filling in the values represented by letters. Calculate present values
to the nearest $.
Year Net cash flow Discount factor Present value
$ 16% $
0 .. B
1 .. .. D
2 .. .. E
3 .. C
4 A ..
Net Present Value = F
A =
B =
C =
D =
E =
F =
(b) The company wishes to calculate the internal rate of return of the project and in order to do this the
net present value at a different rates of interest must be calculated. Estimate the net present value to
the nearest $ using a discount rate of 18%.
Net present value =
(c) Estimate the internal rate of return to one decimal place using the IRR formula
IRR =
344 Question bank
78 A retailer is facing increasing competition from new shops that are opening in his area. He thinks that if he
does not modernise his premises, he will lose sales. A local builder has estimated that the cost of
modernising the shop will be $40,000 if the work is started now. The retailer is not sure whether to borrow
the money and modernise the premises now, or to save up and have the work carried out when he has
sufficient funds in the future. Current forecasts show that if he delays the work for three years, the cost of
the modernisation is likely to rise by 4% per annum.
Investigations have revealed that, if he borrows, he will have to pay interest at the rate of 3% per quarter,
but if he saves the money himself he will only earn 2% per quarter.
Required:
(a) The retailer borrows $40,000 at 3% per quarter, and repays $X at the end of each quarter for three
years.
(i) Use tables to find the present value of the repayments as a function of X.
(ii) Find the value of X to the nearest $.
(b) If the retailer decides to save money at 2% per quarter so that he has sufficient funds to carry out
the work in three years' time, complete the following shaded boxes.
(i) The cost of modernisation in three years' time correct to 2 decimal places.
(ii) If twelve instalments of $Y are invested, the first being paid immediately, use tables to find
the present value of the instalments as a function of Y.
(iii) Use tables to find the value of Y to the nearest $10.
(c) On the basis of the results that you have calculated above, what would you advise the retailer to do?
(Tick as appropriate).
Modernise now
Save and modernise later
79 The correlation between x and y is 0.95. This means that:
A There is a weak relationship between x and y
B There is a strong relationship between x and y
C y is 95% of x
D x is 95% of y
Question bank 345
80 The following scatter diagrams can be associated with which correlation coefficients?
I 0
II –1
III +0.8
A =
B =
C =
81 What is the Pearsonian correlation coefficient, r, for the following data?
X Y
1 6
2 5
3 3
4 8
A –0.25
B –0.06
C +0.06
D +0.25
82 If n = 4
∑X = 10
∑Y = 22
∑X
2
= 30
∑XY = 57
∑Y
2
= 134
The product moment correlation coefficient is
A –0.25
B –0.06
C +0.06
D +0.25
346 Question bank
83 Seven novels were reviewed by two different book critics, and the novels were ranked as follows.
Critic 1 Critic 2
Rank Rank
Captain Corelli's guitar 2 1
Debbie Jones's diary 1 3
The songs of a bird 4 7
Cold love in a warm climate 6 5
Raging wars and peacefulness 5 6
Charlotte Black 3 2
The name of the tulip 7 4
The rank correlation coefficient is
A –0.464
B –0.536
C +0.464
D +0.536
84 In calculating the regression equation linking two variables, the standard formulae for the regression
coefficients are given in terms of X and Y. Which of the following is not true?
I X must be the variable which will be forecast
II It does not matter which variable is which
III Y must be the dependent variable
IV Y must be the variable shown on the vertical axis of a scattergraph
A I and II
B I, II and III
C I, II and IV
D I, III and IV
85 If
∑X = 21
∑Y = 184
∑X
2
= 91
∑XY = 587
n = 7
Which of the following values for a and b are correct in the formula Y = a + bx?
a b
A –22.5 –1.25
B –22.5 +1.25
C +22.5 –1.25
D +22.5 +1.25
86 The regression equation Y = 5 + 4X has been calculated from 6 pairs of values, with X ranging from 1 to 10.
The correlation coefficient is 0.9. It is estimated that Y = 85 when X = 20. Which of the following are true?
I The estimate is not reliable because the sample is small
II The estimate is reliable
III The estimate is not reliable because the correlation is low
IV The estimate is not reliable because X is outside the range of the data
Question bank 347
A I and II only
B I and III only
C I and IV only
D II and IV only
87 When the value of one variable is related to the value of another, they are said to be correlated. Correlation
therefore means an inter-relationship or correspondence.
If the following points were plotted on a graph, what sort of correlation would they display? (Tick as
appropriate)
(a) (2, 3)
(3, 4.5)
(4, 6)
?
Perfect positive correlation
Perfect negative correlation
Uncorrelated
(b) (2, 3)
(3, 1.5)
(4, 0)
?
Perfect positive correlation
Perfect negative correlation
Uncorrelated
(c) (2, 3)
(4, 0)
(4, 6)
?
Perfect positive correlation
Perfect negative correlation
Uncorrelated
88 A small company has recorded the following data on volumes and costs of production for the last ten
months.
X = Production ('000 units) 4 6 9 10 8 5 7 11 12 10
Y = Costs ($'000) 11 12 19 22 20 16 13 24 20 15
Production Costs
Sums
∑X = 82 ∑Y = 172 ∑XY = 1,492
Sums of squares
∑X
2
= 736 ∑Y
2
= 3,136
Required:
(a) If the regression equation of costs (Y) on production (X) = Y = a + bX, calculate the following.
(i) Calculate the value of b to 4 decimal places.
(ii) Calculate the value of a to 2 decimal places.
(b) If the regression equation based on the data given above was calculated to be Y = 7 + 1.5X with a
Pearson correlation coefficient of 0.8, answer the following questions.
(i) What would the fixed costs of the factory be?
348 Question bank
(ii) Plot the regression line Y = 7 + 1.5X on the axes provided.
(iii) Predict the total production costs for next month if an output volume of 10,000 units is
forecast.
89 A company is building a model in order to forecast total costs based on the level of output. The following
data is available for last year.
Month Output Costs
'000 units $'000
(X) (Y)
January 16 170
February 20 240
March 23 260
April 25 300
May 25 280
June 19 230
July 16 200
August 12 160
September 19 240
October 25 290
November 28 350
December 12 200
Question bank 349
Required:
(a) Plot a scattergraph of costs on output using the axes provided below.