A manufacturer recons that the value of a machine which costs him Rs. 125000 will depreciate each year by 20%. Find the estimated value of the machine at the end of 5 years.

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Solution

Short- cut method

$Value of the machine after 5 years = R s . {{(1 - \frac{20}{100})}^{5}} = R s . {125000 \times {(\frac{4}{5})}^{5}} = R s . (\frac{125000 \times 1024}{3125}) = R s . 40960. Hence, the vale of the machine after 5 year is Rs. 40960$

Alternative method

$Intial value of the machine = Rs. 125000 Value fo the machine after 1 year = 80 % o f R s . 125000 = R s . (125000 \times \frac{80}{100}) = R s . 80000. Thus, the yearwise values of the machine are R s . 125000, R s . 100000, R s . 80000, \dots here, \frac{100000}{125000} = \frac{4}{5}, \frac{80000}{100000} = \frac{4}{5}, e t c . thus these amounts from a GP with a = 125000 and r = \frac{4}{5} . Value after 5 years = 6th term = T_{6} = a r^{(6 - 1)} = a r^{5} = R s . {125000 \times {(\frac{4}{5})}^{5}} = R s . (\frac{125000 \times 1024}{3125}) = R s . 40960.$

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