The Value of a Car Depreciated by 10% in the First 2 Years and by 8% in the Third Year. Express the Total Depreciation of the Car as a Single per Cent During the Three Years.

प्रश्न

The value of a car depreciated by 10% in the first 2 years and by 8% in the third year. Express the total depreciation of the car as a single per cent during the three years.

योग

उत्तर

Let value of car be Rs x.

`"V"_0` =Rs x ; n = 3 ; r = 10% for first 2 years and 8% for 3rd year .

`therefore "V"_"t" = "V"_0 xx (1 - "r"/100)^"n"`

`=> "V"_"t" = "Rs" "x" xx (1 - 10/100)^2 (1 - 8/100)`

`=> "V"_"t" = "Rs" "x" xx 9/10 xx 9/10 xx 23/25`

`=> "V"_"t" = "Rs" "x" xx 1863/2500`

`=> "V"_"t" = "Rs" 0.7452 "x"`

Depreciation in the value of car

= Rs (x - 0.7452 x) = Rs 0.2548 x

Percentage change in depreciation

`= (0.2548 "x")/"x" xx 100`

= 25.48 %

Percentage change = 25.48 %

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Concept of Compound Interest - Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years

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