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The value of a machine depreciates at the rate of 10% per annum. If its present value is ₹1,62,000, then what will be its worth after 2 years?
₹1,26,860
₹1,32,860
₹1,31,220
₹1,27,760
₹1,31,220
Use the ratio of 100:90 (or 10:9). For 2 years, apply the square of the ratio: (10:9)2=100:81. Calculate 1,62,000×10081=1,620×81=1,31,220.
Present value of the machine = ₹1,62,000, Rate of depreciation (r) = 10% per annum, Time (n) = 2 years.
A=P×(1−100r)n
Use the ratio of 100:90 (or 10:9). For 2 years, apply the square of the ratio: (10:9)2=100:81. Calculate 1,62,000×10081=1,620×81=1,31,220.
Confusing depreciation with appreciation; using (1+r/100)n instead of (1−r/100)n will result in a higher, incorrect value.
Identify parameters
The present value P=1,62,000, the annual depreciation rate r=10%, and the duration n=2 years.
P=1,62,000,r=10%,n=2
Apply depreciation formula
Substitute the values into the depreciation formula A=P×(1−r/100)n.
A=1,62,000×(1−10010)2
Calculate the value
Simplify the expression: A=1,62,000×(0.9)2=1,62,000×0.81.
A=1,62,000×0.81=1,31,220
C is correct because the depreciated value of the machine after 2 years is calculated to be ₹1,31,220.
This concept is identical to compound interest calculations where the principal amount decreases over time; always use the same formula structure for both.
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