A company purchases a machine for RM 10,000, which is expected to last for five years.
i. What is the future value if the value of the machines depreciates at 20% annually?
ii. What is the annual rate of depreciation if the value is reduced by 50% after 3 years?
Answers
(i) The future value of the machine is Rs. 3276.80.
(ii) The rate of depreciation is 20.63 % per year, if the value of the machine reduces by 50 % after 3 years.
• Given,
Price at which the machine is bought = Rs. 10,000
Time for which it is expected to last = 5 years
• Depreciation is the decrease in value of an asset.
(i) Future value of the machine = ?
• Rate of depreciation = 20 %
• Formula for the depreciated amount of an asset is given as :
A = P { 1 - (R / 100) }ⁿ
Where A is the depreciated value of the asset,
P is the initial value of the asset,
R is the percentage rate of depreciation,
n is the time in years.
• Therefore, depreciated value of the machine after 5 years = Rs. 10,000 { 1 - (20 / 100) }⁵
=> Depreciated value = Rs. 10,000 { (100 - 20) / 100 }⁵
= Rs. 10,000 × (80 / 100)⁵
= Rs. 10,000 × (8 / 10)⁵
= Rs. (10,000 × 85) / 10⁵
= Rs. (10,000 × 8 × 8 × 8 × 8 × 8) / 1,00,000
= Rs. (8 × 8 × 8 × 8 × 8) / 10
= Rs. 32,768 / 10
= Rs. 3276.80
∴ The depreciated value of the machine after 5 years = Rs. 3276.80
(ii) Rate of depreciation = ?
• Percentage of reduction in value after 3 years = 50 %
∴ Reduced price = (100 - 50) % of Rs. 10,000
= 50 % of Rs. 10,000
= (50 / 100) × Rs. 10,000
= Rs. 10,000 / 2
= Rs. 5000
• Now,
Rs. 5000 = Rs. 10,000 { (1 - rate %) / 100 }³
=> Rs. 5000 = Rs. 10,000 × { (100 - rate %) / 100 }³
=> Rs. 5000 / Rs. 10,000 = (100 - rate %)³ / (100)³
=> 1 / 2 = (100 - rate %)³ / 10,000,00
=> (1 × 10,000,00) / 2 = (100 - rate %)³
=> 10,000,00 / 2 = (100 - rate %)³
=> 5,00,000 = (100 - rate %)³
=> 500 × 1000 = (100 - rate %)³
=> ∛500 × ∛1000 = 100 - rate %
=> 7.937 × 10 = 100 - rate %
=> 79.37 = 100 - rate %
=> rate % = 100 - 79.37
=> rate = 20.63 %
∴ The rate of depreciation is 20.63 % per annum.