A machine costs ₹5,00,000. If the value depreciates 15% in the first year, 13 1/2 % in the second year, 12% in the third year and so on. What will be its value at the end of 10 years, when all the percentages will be applied to the original cost?
Answers
Answer:
Value at the end of 10 years = Rs 87500
Step-by-step explanation:
All depreciation are on original value
original Value = 500000
Depreciation of 1 st year = 500000 * 15 * 1/100 = Rs 75000
Depreciation of 2nd year = 500000 * 13.5 * 1/100 = Rs 67500
Depreciation of 2nd year = 500000 * 12 * 1/100 = Rs 60000
This is an AP
Where first Term = a = 75000
Common difference = d = -7500
n = 10
Sum of all depreciation = (n/2)(a + a + 9d)
= (10/2)( 150000 -9*7500)
= 5 * 82500
= 412500
value at the end of 10 years = 500000 - 412500 = 87500
Value at the end of 10 years = Rs 87500
Step-by-step explanation:
cost of machine = 5,00,000
rate of depreciation
= 15%,13 1/2 % , 12% ....
here a = 15 ,d = 13 1/2"% - 15% = -1.5%
rate of depreciation in the 10th year
= a + 9d=15% + 9(-1.5%)=15-13.5=1.5%
total value depreciated in 10 years
= 15%+13.5% + 12% +......+1.5%
here last term l= 1.5% , first ,a = 15
Use Sn = n/2 * (a + l)
so S10 = 10/2 ( 15 + 1.5) = 82.5%
total value depreciated in 10 yrs
= 82.5%
value remaining
=100% - 82.5% = 17.5%
value of Machine at the end of 10 years
= 17.5% of 5,00,000
=0.175 × 5,00,000 = Rs 87500 Answer