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OCUS ON WORKING MATHEMATICALLY

In Australia, interest rates were increased twice in 2003 and again in March 2005 to try to discourage people from borrowing too much. Nevertheless, inflation in Australia is low and we have a very strong economy.

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How do we measure inflation?

The first activities are designed for discussion in class or in small groups.

1 The Consumer Price Index (CPI) is the official measure of inflation in Australia. The CPI is measured every 3 months and published by the Australian Bureau of Statistics. It is a measure of the cost of living based on the prices of goods and services in 10 main groups.

Three of these groups are food, clothing and footwear, and transport. Discuss other items you would include in the CPI and make a list. What might the other main groups be?

2 Every item in a group has a weighting based on its relative importance. For example in the food category, takeaway and fast foods might have a weighting of 1.2%, while vegetables might be 0.4%. What might this imply about the relative importance of these two items in the CPI at that time?

3 The price index of an item in any group is given by the formula

Find the price index of a cheeseburger which cost $2.50 in 2004 and $3.50 in 2005.

4 In question 3, the year in which the old price was taken is the base year. What was the base year for the price index of the cheeseburger? Explain why the price index of an item in the base year is always 100.

5 The Australian Bureau of Statistics computes the CPI every quarter for each capital city and then computes a national weighted average. It is the change in the CPI that measures inflation, and it may be up or down on the base year. Here is the published percentage change in the CPI for the March quarter 2004 to the March quarter 2005.

Weighted average of eight capital cites % change in CPI Mar 2004–2005

Food 0.8

Alcohol & tobacco 3.7

Clothing & footwear −1.9

Housing 4.0

Household furnishings, supplies & services −0.8

Health 5.7

Transportation 2.9

Communication 1.5

Recreation 1.6

Education 6.2

Miscellaneous 2.6

All groups 2.4

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price index new price old price ---×100

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FOCUS ON WORKING MATHEMATICALLY

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OCUS ON WORKING MATHEMATICALLY What was the rate of inflation for this period? What particular groups contributed most to

the change? How might you account for the rise of the CPI for some items and a fall for others?

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In 2002 Finn invested $5000 for 3 years at 4.5% compound interest. Assuming an inflation rate of 2.4% p.a. over the 3 years, what was the real value of her investment at maturity?

Compare the solutions to the problem below and argue a case for your choice.

Solution 1

Using the compound interest formula A= P(1 + R)ⁿ, P= 5000, R = 0.045, n = 3 By calculator: A= $5705.83

However, because of inflation the value of her money is worth less by 2.4%.

So the real value is only 97.6% of $5705.83.

By calculator, A= $5568.89 Solution 2

Finn earns 4.5% interest each year but loses 2.4% each year because of inflation.

Her overall gain is only 2.1%. Using the formula, P= 5000, R = 0.021, n = 3 A= $5321.66

Solution 3

Finn’s balance on paper at the end of 3 years is $5705.83 (see solution 1).

However over 3 years $5000 depreciates 2.4% each year. The depreciation is given by the formula A= P(1 − R)ⁿ where P= 5000, R = 0.024 and n = 3. By calculator this comes to

$4648.57. Her loss due to inflation is therefore $351.43 Answer: A= $5705.83 − $351.43 = $5354.40

2 Visit the Australian Bureau of Statistics website <www.abs.gov.au> and click on Consumer Price Index Australia. Compare the capital cities for inflation rates and the items which had the most effect on the CPI for the latest data available. Why does it cost more to live in some cities than others?

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Make a class poster to illustrate what you have learned about inflation in this exercise.

Summarise the important points in your workbook.

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It is really important to understand how you can use mathematics to manage your finances.

How you manage your income and your spending will determine your lifestyle, whether you earn a lot or have a modest income. Your future happiness will depend on it.

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1 Without using formulas explain simply the difference between simple and compound interest.

2 What is a credit card? Is the interest charged simple or compound?

3 What is the CPI? What does it measure?

4 What is the difference between a wage and a salary? Name two occupations where people are paid wages, and two that are paid salaries.

5 Read the Macquarie Learners Dictionary entry for budget:

budgetnoun 1. a plan showing how much money a person, organisation or country will earn and how it will be spent

–verb 2. to make such a plan: We budgeted on the basis that we would both have full-time jobs next year.

–adjective 3. not costing much: budget clothes.

❐ Word Family: budgetary adjective

Does the mathematical meaning differ from that in everyday speech?

1 Calculate the simple interest earned on the following investments.

a $300 at 5% p.a. for 2 years b $450 at 7.5% for 3 years c $785 at 6.2% p.a. for 8 years d $1200 at 4 % for 5 years

2 Find the total balance of an account after 4 years if $2000 is invested at 6% p.a.

simple interest.

3 Calculate the simple interest that would be earned on the following investments.

a $700 at 8% p.a. for 6 months b $840 at 6.5% p.a. for 9 months c $1500 at 7.25% p.a. for 5 months 4 Brian invested $600 with a building

society for 3 years, with simple interest paid at 5% p.a. He then transferred the principal and interest to a bank account

for 2 years and was paid simple interest at the rate of 5.8% p.a.

a How much money did Brian have at the end of the 5th year?

b How much interest did he earn altogether?

5 Louise invested an amount of money for 6 years at 4% p.a. simple interest.

She earned $192 in interest on this investment. How much did she invest?

6 Rachel deposited $12 000 in a savings account. After 8 years she had earned

$6720 in simple interest. Find the annual interest rate.

7 A sum of $20 000 was invested for 3 years at 5% p.a. compounded annually.

Draw up a compound interest table and hence find the account balance after:

a 1 year b 2 years c 3 years

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