A manufacturer reckons that the value of a machine, which costs him Rs 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.

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Solution

The value of machine will depreciate each year by 20%. The initial cost of the machine is Rs. 15625.

Let the rate through which machine depreciates be R.

R=20%

The value V of machine after one year is given by,

V= 100−20 100 ×15625 = 80 100 ×15625 = 4 5 ×15625

The value remains 4 5 of its initial cost.

The value of machine at the end of 5 years is given by,

V 5 =15625× 4 5 × 4 5 ×…5 times =15625× ( 4 5 ) 5 =15625× 1024 3125 =5×1024

Further simplify the above expression.

V 5 =5120 Rs.

Thus, value of machine at the end of 5 years is Rs.5120.

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