Inflation
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.
A = P(1 + r)n
Where A is the final amount
P is the initial price
r is the inflation rate
n is the number of years
Appreciation
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.
A = P(1 + r)n
Where A is the final amount
P is the initial price
r is the inflation rate
n is the number of years
Example 1
The price of hamburgers rises at a constant 6% pa.
What will a $4 hamburger be worth in 3 years?
A= ?
A = P(1 + r)n
P = $4
= 4 × (1 + 0·06)3
r = 0·06
= $4·76
n=3
Example 2
The 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 = 6·75
A = P(1 + r)n
P=?
6·75 = P(1 + 0·028)8
r = 0·028
6·75 = P × 1·2472
n=8
P = 6·75  1·2472
P = $5·41
Example 3
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 = 10·10
A = P(1 + r)n
P = 7·20
10·10= 7·20 × (1 + 0·07)n
r = 0·07
1·07n = 10·10  7·20
n=?
1·07n = 1·40278
Either use guess and check
Guess and check.
Let n = 4
1·074 = 1·31
To small
Let n = 6
1·076 = 1·50
To big
Let n = 5
1·075 = 1·40
Just right
n = 5
Example 4
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)
A=
P=
r =
n=
1310.12
1100.00
?
3
A = P(1 + r)n
1310.12 = 1100 × (1 + r)3
Example 4
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)
A=
P=
r =
n=
1310.12
1100.00
?
3
A = P(1 + r)n
3
1310.12 = 1100 × (1 + r)
1310.12
3
 1 r
1100
3
1310.12
 1 r
1100
1.06000647
...1 r

1.061 r
r  0.06
Therefore the
 average rate of
inflation is 6%.
Today’s work
Exercise 8G page 289
#1e, 4, 6a, 8, 10, 12, 13