Maths Quest Maths A Year 12 for Queensland
WorkSHEET 2.1
Chapter 2 Appreciation and depreciation WorkSHEET 2.1
1
Appreciation and depreciation
Name: ___________________________
1
If the inflation rate is 3% p.a., estimate the cost Price next year = 103% of $28 000
next year of a new car which has a price tag of
= $28 840
$28 000 this year.
2
If inflation continues to grow at 3% p.a. for the
next 5 years, what would be the price of the car
from question 1 in 5 years’ time.
P  $28 000
R  3% p.a.
n 1
T 5
/50
3
5
nT
R 

A  P 1 

 100  n 
1 5
3 

 28 0001 

 100  1 
3 

 28 0001 

 100 
 $32 459.67
3
A valuable coin, purchased for $250, is
expected to grow in value by 10% p.a. Give an
estimate of the value of the coin in 10 years’
time, correct to the nearest $10.
5
P  $250
R  10% p.a.
n 1
T  10
5
nT
R 

A  P 1 

 100  n 
1  10
10 

 2501 

 100  1 
10
10 

 2501 

 100 
 $650 to the nearest $10
4
A block of land was available for sale last year
at $35 000.
(a) If the inflation rate during the year was
3.2%, what would be the value of the
land this year?
(b)
If the inflation rate this year is reduced to
2.7%, what price would the land attract
next year?
(a)
Price last year  $35 000
Price this year  103.2% of $35 000
 $36 120
(b)
Price this year  $36 120
Price next year  102.7% of $36 120
 $37 095
5
Maths Quest Maths A Year 12 for Queensland
5
Chapter 2 Appreciation and depreciation WorkSHEET 2.1
A new car worth $50 000 depreciates by $6000 (a)
per year.
(a) Complete the table below to show the
change in the value of the car over a
5-year period.
Age (years)
Value ($)
(b)
(c)
0
(new)
50 000
8
Age
(years)
Value ($)
0
(new)
1
2
3
4
5
50 000 44 000 38 000 32 000 26 000 20 000
(b)
1
2
3
4
5
Graph the age of the car (on the x-axis)
against the value of the car (on the
y-axis).
Use your graph to determine the age of
the car when it could be ‘written off’
(i.e. have no value).
(c)
6
2
Extending the line to determine the age of the
car when it is $0 in value gives an estimated
age of 8 13 years.
The depreciation on a $3500 computer package
is shown in the table below.
Age
(years)
0
(new)
1
2
3
4
5
Value ($)
35 000
2975
2530
2150
1830
1550
7
Draw a graph of age (on the x-axis) against the
value (on the y-axis). Draw a smooth curve
through the points. Extend this curve and
estimate the value of the computer when it is
8 years old.
From the curve, the computer has a value of
approximately $950 when it is 8 years old.
7
A $200 000 bus coach depreciates at the rate of
$15 000 per year. Calculate the salvage value
of the coach after 5 years.
S  V0  Dn
 200 000  15 000  5
 200 000  75 000
 $125 000
So, the coach has a salvage value of $125 000
after 5 years.
5
Maths Quest Maths A Year 12 for Queensland
8
Chapter 2 Appreciation and depreciation WorkSHEET 2.1
After how many years would the coach in
question 7 have a salvage value one-quarter of
its original value?
New value  $200 000
3
4
1
of $200 000  $50 000
4
S  V0  Dn
50 000  200 000  15 000  n
15 000 n  $150 000
n
150 000
15 000
 10
So, the coach would be worth one-quarter of its
original value after 10 years.
9
The price of a new car is $25 000. Its value
depreciates by $250 each month.
Calculate the salvage value of the car after
5 years.
Depreciati on  $250 per month
4
 $250  12 per year
 $3000 per year
S  V0  Dn
 25 000  3000  5
 $25 000  $15 000
 $10 000
So, the salvage value of the car after 5 years is
$10 000.
10
The car in question 9 is driven until its salvage
value is $0. What would be its age at this stage?
S  V0  Dn
0  25 000  3000  n
3000 n  25 000
25 000
n
3000
n  8 13 years
So, when the car is 8 13 years old, its salvage
value will be $0.
4