Question 1 [4 marks]
The following data was collected about fifty year old workers giving their salary (£’000s) denoted by x and their savings (in £'000s) denoted by y.
(There are 7 data pairs so n = 7.)
[Use x= 22 etc and y= 8 etc throughout. You do not need x= 22000 etc, y= 8000 etc]
WorkerABCDEFG
x22253028443350
y852540901580
Calculate
1)the mean of x (to 3 dp), 33.143 to 3 dp
2)the correlation coefficient, r (to 3 dp) . to 3 dp
The equation of the regression line is y = A + Bx, calculate (to 3dp) the values of:
3) B to 3 dp
4) A to 3 dp
Question 2 (6 marks)
You are investigating the effect of advertising on sales. You draw a scatter plot and obtain the regression
line y = 4.3 + 1.8x where x is the amount spent on advertising and y is the value of sales.
For this regression line state
1)the gradient,1.8
2)the y-intercept.4.3
3)If advertising is increased by 10 units, how many units is the value of sales increased by?
4)Use the regression line to predict the sales when 40 units is spent on advertising.
For each of the two statements below decide if you think the statement is true (enter 1) or false (enter 2).
5)“The y-intercept is the money spent on advertising when the value of sales is zero.” 1 or 2
6)“The gradient is the increase in the value of sales when one more unit is spent on advertising.” 1 or 2
Question 3 (3 marks)
A sum of £24000 is invested to earn compound interest at a rate of 3.2% per annum.
1)Calculate the interest earned in the first year.35024.15 to 2dp, no £ sign, no commas
2)Calculate the amount in the account after 6 years. 28992.75 to 2dp, no £ sign, no commas
3)After how many years will the amount in the account first exceed £40000? 17
Question 4 (2 marks)
Use the Payback Method to answer this question.
The cash flows for Project 8 and Project 9 are as shown.
YearProject 8Project 9
0-10000-10000
136002300
233004200
330002100
410001300
57001200
6300800
Work out which project will repay the initial investment earlier and in which year.
1)Project8 8 or 9
2)Year4 1, 2, 3, 4, 5, or 6
Question 5 (2 marks)
£1250 is spent on a credit card and 1.8% interest is charged monthly.
1)If no payments are made calculate how much is owed at the end of two years. 1918.03 to 2dp, no £ sign, no commas
2)Calculate the A.E.R. giving your answer as a percentage correct to 2dp. to 2dp, no % sign
Question 6 (3 marks)
A project has the cash flows (in pounds) shown in the (incomplete) table below.
The discount rate is 8% p.a.
YearCash InCash OutCash FlowDiscount FactorPresent Value
0030001
12700800
242001100
31600900
Calculate
1)the discount factor applied in Year 3, to 4dp
2)the present value of the Year 2 cash flow, to 2 dp, no £ sign
3)the net present value (NPV) of the project.nearest £, no £ sign, no commas