MAT112 BUSINESS MATHEMATICS
CHAPTER 9 (DEPRECIATION)
1. Delicious Bakery bought a microwave oven at RM17,000. It is estimated to last for 7
years and has a salvage value of RM3,000.
i) Find the book value of that oven after 3 years by using the straight line method.
[RM11,000]
D=(17000-3000)÷7
=RM2,000
BV3=17000-3(2000)
=RM11,000
ii) Find the annual rate of depreciation by using the declining balance method.
[21.95%]
(Q5(a) Oct 2012)
𝟑𝟎𝟎𝟎
r =[1- 7√𝟏𝟕𝟎𝟎𝟎 ] ×100
= 21.95%
2. A plasma television costs RM5888 and has an expected life of 7 years. After 3 years of
usage, the total depreciation of the television using declining balance method was
RM1595.65.
i) Find the rate of the depreciation. [10%]
(𝟓𝟖𝟖𝟖−𝟏𝟓𝟗𝟓.𝟔𝟓)
r =[1- 3√ 𝟓𝟖𝟖𝟖
] ×100
= 10%
ii) Find the scrap value of the television. [RM2816.21]
(Q5(a) March 2012)
SV=5888(1-0.1)7
=RM2,816.21
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3. A machine has a scrap value of RM12,000 at the end of 8 years and the book value of
RM14,000 at the end of 6 years. Using the straight line method, find the cost of the
machine. (RM20,000)
(Q5(a) Sept 2011)
D=(14000-12000)÷2
=RM1,000
BV6=C-6(1000)
14000=C-6000
C=RM20,000
4. The cost of a grass cutter is RM8,000 and its salvage value at the end of 7 years is
RM1,7000. Calculate the accumulated depreciation and the book value of the cutter at
the end of 4th year using the straight line method. (AD4 = RM3,600, BV4 = RM4,400)
(Q5(b), Sept2011)
D=(8000-1700)÷7
=RM900
AD4=4(900)
=RM3,600
BV4=8000-3600
=RM4,400
5. The cost of a car is RM5,000 with useful life of 7 years. The scrap value is estimated to
be RM12,000. Construct a depreciation schedule by indicating the annual depreciation
and the book value for the first 3 years using the declining balance method.
(Q5(c) Sept2011)
D=(50000-12000)÷7
=RM
6. The cost of a new HiFi is RM3,850. Its estimated useful life is 5 years with a scrap value
of RM650. Find
i) The accumulated depreciation for 3 years using the straight line method.
D=(3850-650)÷5
=RM640
DA3=3(640)
=RM1,920
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ii) The annual rate of depreciation using declining balance method.
𝟏𝟗𝟑𝟎
r =[1- 3√ ] ×100
𝟑𝟖𝟓𝟎
=20.56%
iii) The book value of HiFi at the end of 3 years using sum of digit method.
(Q5(a) April2011)
7. A factory purchased a machine at price RM165,000. The machine has an expected life
of 15 years. lt will then have a scrap value of RM15,000. Find the book value after 5
years using:
i) the straight-line method. (RM115000)
D=(165000-15000)÷15
=RM10,000
BV5=165000-5(10000)
=RM115,000
ii) the sum-of-years-digits method. (RM83750)
(Q5(a) oct2010)
8. A new machine which costs RM15,000 is expected to have a useful life of 5 years and a
scrap value of RM4.000. Calculate the book value of the machine at the end of the third
year using the:
i) straight line method (RM8400)
D=(15000-4000)÷5
=RM2,200
BV3=15000-3(2200)
=RM8,400
ii) sum of year digits method.(RM6200)
(Q5(a) apr2010)
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9. Sedap Restaurant bought a water dispenser for RM1,500. The estimate useful life of the
water dispenser is 5 years and its salvage value is RM200. What is the amount of
depreciation at the end of the fourth year using the straight line method?(RM1040)
(Q5(a) oct2009)
D=(1500-200)÷5
=RM260
DA4=4(260)
=RM1,040
10. The manager of a transport company estimates that the value of its vehicles will
depreciate at an annual rate of 15% based on the declining balance. How long does it
take for a vehicle to have a book value of RM5,000 if the cost was
RM60,000?(15.3years)
(Q5(b) oct2009)
5000=60000(1-0.15)n
0.0833=0.85n
log 0.083 = n log 0.85
n=15.3 years
11. The cost of a new station wagon is RM90000. It is estimated to have a useful life of 10
years with a scrap value of RM20,000. Using the declining balance method, find the
book value and accumulated depreciation at the end of eight years.(BV8 = RM27029.98,
AD8 = RM62970.02)
(Q5(a) apr2009)
𝟐𝟎𝟎𝟎𝟎
r =[1- 10√𝟗𝟎𝟎𝟎𝟎 ] ×100
=13.96%
BV8=90000(1-0.1396)8
=RM27,029.98
AD8=90000-27029.98
=RM62,970.02
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12. The cost of a machine is RM7000 and its salvage value is RM800 at the end of 9 years.
Calculate the depreciation and the book value for the 4th year using the straight line
method. (D = RM688.89 , BV4 = RM4244.44)
(Q5(b) apr2009)
D=(7000-800)÷9
=RM688.89
BV4=7000-4(688.89)
=RM4,244.44
13. A laser printer costing RM6000 has a life expectancy of 6 years and a salvage value of
RM800. Using the declining balance method, calculate the depreciation for the third
year.(RM874.32)
(Q5(a) oct2008)
𝟖𝟎𝟎
r =[1- 6√𝟔𝟎𝟎𝟎 ] ×100
=28.52%
D3= 0.2852(6000)(1-0.2852)3-1]
=RM874.32
14. An exercise machine is estimated to have a life expectancy of 5 years and its salvage
value is RM900. Using the sum-of-year digits method, calculate the cost of the machine
if depreciation for the second year is RM560.(RM3000)
(Q5(b) oct2008)
15. Motorbike.com bought a motorcycle for RM30000. The motorcycle has a life expectancy
of 10 years with a scrap value of RM8000. After 3 years, the motorcycle was sold for
RM20000. Calculate the difference between the book value and the amount received
from selling the motorcycle if Motorbike.com uses
i) the straight line method.(RM3400)
D=(30000-8000)÷10
=RM2,200
BV3=30000-3(2200)
=RM23,400
BV3-SP=23400-20000
=RM3,400
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ii) the reducing balance method.(RM180.46)
(Q5(a) apr2008)
𝟖𝟎𝟎𝟎
r =[1- 10√ ] ×100
𝟑𝟎𝟎𝟎𝟎
=12.38%
BV3=30000(1-0.1238)3
=RM20,180.46
BV3-SP=20180.46-20000
=RM180.46
16. Amran wants to sell his car that has been used for 5 years. The car was bought for
RM93555. The scrap value after 15 years was estimated to be RM10000. Two second-
hand car dealers offered to sell his car. VML Trading Sdn. Bhd. used the declining
balance method while GXL Enterprise used the sum-of-year-digits method to calculate
the depreciation.
i) Find the book value at the end of four years for both
companies.(VML:RM51533.32 , GXL:RM55955.25)
𝟏𝟎𝟎𝟎𝟎
r =[1- 15√𝟗𝟑𝟓𝟓𝟓 ] ×100
=13.85%
BV4=93555(1-0.1385)4
=RM51,533.32
ii) Which car dealer should Amran choose to sell his car? State your reason. (GXL :
offers higher selling price)
(Q5(a) oct2007)
17. Sail Stationery Company bought a copying machine at RM12000. The company expects
to use it for 5 years. It will then have a scrap value of RM2000. Using the reducing
balance method, calculate
i) the annual rate of depreciation (30.12%)
𝟐𝟎𝟎𝟎
r =[1- 5√𝟏𝟐𝟎𝟎𝟎 ] ×100
=30.12%
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ii) the book value at the end of the 3rd year. (RM4095.35)
(Q5(a) apr2007)
BV3=12000(1-0.3012)3
=RM4,094.87
18. A set of equipment for a Photo Shop was bought for RM100,000 and has a useful life of
10 years. If the scrap value is RM10000, calculate the depreciation for the 4th year
using:
i) the sum-of-years-digits method. (RM11454.55)
ii) the straight-line method. (RM9000)
(Q5(b) apr2007)
D=(100000-10000)÷10
=RM9,000
D4=RM9000
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