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Prices for goods, services and wages increase over time. In Australia we measure inflation by using the CPI (consumer price index). The CPI measures the change in price over time of a “weighted basket of goods” that the average household would use.
The RBA (Reserve Bank of Australia) has a 2% to 3% range for inflation and uses interest rates as one method of controlling inflation.
As inflation rises the purchasing power of your money is reduced. You need to take this into account when planning your investments.
If the inflation rate is constant, you can use the compound interest formula to find the final value.
Inflation
A = P(1 + r)n
Where A is the final amountP is the initial pricer is the inflation raten is the number of years
Most items, such as cars, depreciate over time. That is their value goes down.
Some items, such as antiques or property, may appreciate over time. That is their value goes up.
If the rate of appreciation is constant, you can use the compound interest formula to find the final value.
Appreciation
A = P(1 + r)n
Where A is the final amountP is the initial pricer is the inflation raten is the number of years
Example 1The price of hamburgers rises at a constant 6% pa.What will a $4 hamburger be worth in 3 years?
A = P(1 + r)n
= 4 × (1 + 0·06)3
= $4·76
Example 2The price of a ream of paper is $6·75. If paper has increased at the constant rate of 2·8% pa for the past 8 years, what was a ream of paper worth 8 years ago?
A = P(1 + r)n
6·75 = P(1 + 0·028)8
6·75 = P × 1·2472 P = 6·75 1·2472 P = $5·41
A =P = r =n =
?$40·063
A =P = r =n =
6·75?0·0288
Example 3
A = P(1 + r)n
10·10= 7·20 × (1 + 0·07)n
1·07n = 10·10 7·201·07n = 1·40278
The price of Tea Tree Oil rises at a constant rate from $7·20 to $10·10.How many years did it take if the rate was 7%?
A =P = r =n =
10·107·200·07?
Either use guess and checkGuess and check.Let n = 41·074 = 1·31To smallLet n = 61·076 = 1·50To big
Let n = 51·075 = 1·40Just rightn = 5
Example 4
A = P(1 + r)n
1310.12 = 1100 × (1 + r)3
The price of an antique ring three years ago was $1100. It is now worth $1310.12. Calculate the average yearly inflation rate which would produce this appreciation.
A =P = r =n =
1310.121100.00?3
a)
Example 4
A = P(1 + r)n
1310.12 = 1100 × (1 + r)3
The price of an antique ring three years ago was $1100. It is now worth $1310.12. Calculate the average yearly inflation rate which would produce this appreciation.
A =P = r =n =
1310.121100.00?3
a)
€
1310.12
1100= 1+ r( )
3
€
1310.12
11003 =1+ r
€
1.06000647... =1+ r
€
1.06 −1 = r
€
r = 0.06
Therefore the average rate of inflation is 6%.
Today’s workExercise 8G page 289#1e, 4, 6a, 8, 10, 12, 13
