Rising costs
It’s quite clear that the cost of food
is rising. Soon we won’t be able to
afford to eat, let alone drive a car!
Everything costs more,
but some things seem
to cost a lot more. How
can we tell how much
prices have risen by?
Rising costs
The Retail Price Index looks at the changes in the
cost of a combination of: food, heating, housing,
household goods, bus fares and petrol costs.
The figures on the next slide show the ratios of
how these costs have increased since 1993.
For each £100 in 1993, the equivalent cost in 2013
is £178.
Rising costs
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
1.00 1.02 1.06 1.09 1.12 1.16 1.18 1.21 1.24 1.26 1.29
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
1.33 1.37 1.40 1.46 1.52 1.52 1.58 1.66 1.73 1.78
• When did costs rise quickest?
• In what year would you expect costs to be
double those of 1993?
Rising costs
Which items have increased most
in price since 1993?
1993
price
Average house price
£68,032
1 litre of unleaded petrol
50p
Loaf of bread
39p
First class stamp
25p
A pint of milk
34p
Predicted
2013 cost,
using RPI
Real 2013
Percentage
price
increase from
1993 to 2013
Rising costs
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
1.00 1.02 1.06 1.09 1.12 1.16 1.18 1.21 1.24 1.26 1.29
From 1995 to 1997 the increase
was 3% each year, so each year
people paid 3% more for things
than they paid the year before.
…is that
true?
Better off or not?
I think we’re
better off now
than a few years
ago…
What does it mean to
be ‘better off’?
What data would we
need to be able to tell
if we are better off?
Better off or not?
• People attach different meanings to the phrase
‘better off’. The list of possible measures is very
diverse.
• Measures might include: economic well being,
employment rates, home ownership, crime
rates, educational achievements, amount of free
time people have, how happy people are…
• What would you include?
Better off or not?
• One way to decide whether we are generally
financially better off is to look at ‘discretionary
income’.
• This is an estimate of how much money each
household has left after paying all taxes and
essential living costs including rent or mortgage,
fuels and electricity, food, insurances etc.
Better off or not?
• Data about discretionary income are difficult to
calculate and locate, but one supermarket chain
provides the following information:
Average discretionary income per household per week
£
2008
148.00 £
2009
161.00 £
2010
158.00 £
2011
145.00 £
2012
147.00
• Can we simply compare the average amount of
money a household has available each year to
what they had the previous year?
• If not, how could we compare them?
Can we afford it?
We’d like to buy a new car,
but will need to take out a
loan. There are lots of loans
around that don’t make you
pay much back each month.
Should it
matter how
much we pay
back in total?
Can we afford it?
• Assuming that the couple wish to borrow
£10,000 over 2, 3 or 5 years. Several options
are available to them.
• They might consider borrowing money from the
following sources:
– Bank (personal loan)
– Online ‘payday’ loan
– Credit card
• APR is the Annual Percentage Rate, can you
find an APR for each type of loan?
Can we afford it?
• How much would they pay each month using
each type of borrowing?
• How much would they pay back in total using
each type of loan?
• What would you advise the couple to do?
• This will help to check your findings!
Teacher notes:
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•
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These activities target the following content and skills:
– Using percentages
– Understanding ratios and percentages
– Plotting graphs and predicting values
– Using real life contexts
– Understanding and reasoning with data
– Problem solving
Most activities encourage students to think and discuss both their thoughts on the mathematics
and the real world aspects of the problem
Some activities are more challenging than others
Teacher notes: Rising costs
•
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The aims of this activity are to help students consider how year on year comparisons are made to
determine the rate at which prices increase.
You might ask students to think about changes in diet and how a ‘typical’ basket of shopping
might alter over time, within different cultures and also in response to food standards issues
arising such as ‘egg and salmonella’, ‘mad cow disease’ and ‘horsemeat’.
Slide 4: these are the January values from each year taken from data from the Office of National
Statistics
Plotting and extrapolating the data will enable students to predict when the RPI has doubled the
1993 values. However, extrapolating from more recent years gives a prediction of 2016, whereas
predicting using a ‘line of best fit’ leads to a prediction of 2018. (see next slide)
Slide 5: Ideally, students should look up the current costs. March 2013, guideline prices are:
– Average UK house price: £238,000
– 1 litre of unleaded petrol: £1.38
– Loaf of bread: £1.35
– First class stamp: 60p
– A pint of milk: 49p
See slide 18 for answers based on these prices.
The connection between ‘percentage increase’ and RPI ratio will need to be made i.e.276% is
equivalent to an RPI ratio of 2.76
Slide 6: A common misconception. Although each year increases by 3%, this is 3% of the 1993
value, which means that the year to year percentage increases are actually as follows:
1993
1994
2.47
1995
3.33
1996
2.88
1997
2.80
1998
3.30
1999
2.45
2000
1.96
2001
2.70
2002
1.29
2003
2.94
RPI data plotted
RPI based on 1993 value
2.10
2.00
1.90
1.80
1.70
RPI
1.60
1.50
1.40
1.30
1.20
1.10
1.00
0.90
1990
1992
1994
1996
1998
2000
2002
2004 2006
Year
2008
2010
2012
2014
2016
2018
2020
Price comparison answers
1993
price
Average house price
£68,032
Predicted
2013 cost,
using RPI
Real 2013
Percentage
price
increase from
1993 to 2013
£121,096.96 £238,000.00
349.84
1 litre of unleaded petrol
50p
£0.89
£1.38
276.00
Loaf of bread
39p
£0.69
£1.35
346.15
First class stamp
25p
£0.45
£0.60
240.00
A pint of milk
34p
£0.61
£0.49
144.12
Teacher notes: Better off or not?
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Slides 7 & 8: These slides encourage students to consider what is meant by ‘better off.
Slide 10: Can we simply look at the amount of discretionary income? No, we also have to
consider that the cost of living has increased. One way to do this is to use the given values of the
RPI based on the 1993 value and simply divide to find out how much the equivalent discretionary
income would have been in 1993.
Year
Discretionary
income
£
RPI
Comparative
1993 values £
•
2008
2009
2010
2011
2012
148.00 £
1.52
161.00 £
1.52
158.00 £
1.58
145.00 £
1.66
147.00
1.73
97.37 £
105.92 £
100.00 £
87.35 £
84.97
These data suggest that household are worse off now than they were in 2008, which supports the
idea that we are in recession.
Teacher notes: Can we afford it?
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Slide 11: Students may not be familiar with the fact that it is possible to borrow money from
different sources, and that the repayment amounts vary considerably. Although paying off a loan
over a longer term results in lower monthly payments, the total amount paid back increases.
Students should also be made aware that ‘payday’ loans tend to have extremely high APRs and
the amount to repay often increases dramatically for longer repayment terms.
Slide 12: If possible, search for the values online in front of the students, or ask them to find them.
The ‘payday’ loan APR will otherwise seem unbelievable compared to the others.
Typical values are:
– Bank: APR 7.9%
– Online ‘payday’ loan: APR 2689% to 4214%
– Credit card: APR 18.9%
Slide 13: At the bottom of the slide is a link to an online repayment calculator. This will allow all
students to access the problem, even if they struggle with working out the values. Ask students to
draw up a table of values to compare 2 years, 3 years and 5 years as typical lengths of time that
people borrow money for.
The values obtained will beg the question: “Why would people choose a ‘payday’ loan?”
The reasons are varied but include: not having a good credit rating, not having access to banking
facilities, not wishing to fill in forms.
It is important to emphasise that they are really designed to be very short term loans – days rather
than years, but, because of the high interest rate, people can get into more financial difficulties
very quickly with this type of loan.
Teacher notes: data sources used
RPI data: http://www.ons.gov.uk/ons/taxonomy/index.html?nscl=Retail+Prices+Index
Supermarket prices: http://www.mysupermarket.co.uk/#/shopping/findproducts.aspx?query=milk
House prices: http://news.bbc.co.uk/1/shared/spl/hi/in_depth/uk_house_prices/html/houses.stm
Petrol prices: http://www.theaa.com/public_affairs/reports/Petrol_Prices_1896_todate_gallons.pdf
Discretionary income data:
http://your.asda.com/system/dragonfly/production/2012/11/15/10_21_32_928_ASDA_Income_Tracker
_Nov_2012.pdf
APR data:
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https://www.wonga.com/
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http://www.rbs.co.uk/private/loans-cards/g1/loans.ashx
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http://www.barclaycard.co.uk/personal/credit-cards