Question

The cost of a refrigerator is 9000. Its value depreciates at the rate of 5% every year.
Find the total depreciation in its value at the end of 2 years.
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Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf \Rrightarrow The \: cost \: of \: the \: refrigerator \: (Principal) = Rs. \: 9000$

$\sf \Rrightarrow Rate \: of \: the \: value \: depreciated = 5 \: \%$

$\sf \Rrightarrow Time \: of \: depreciation = 2 \: years$

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf \Rrightarrow Total \: depreciation \: after \: 2 \: years = \: ?$

$\bf \underline{ \underline{\maltese\:Solution } }$

$\underline{\boxed{\sf Amount\:Depreciated = P \bigg(1-\dfrac{R}{100}\bigg)^{n}}}$

$\sf Substitute \: the \: values,$

$\sf \implies 9000 \bigg(1-\dfrac{5}{100}\bigg)^{2}$

$\sf \implies 9000 \bigg(1-\dfrac{1}{20}\bigg)^{2}$

$\sf \implies 9000 \bigg(\dfrac{20 - 1}{20}\bigg)^{2}$

$\sf \implies 9000 \bigg(\dfrac{19}{20}\bigg)^{2}$

$\sf \implies \cancel{9000} \times \dfrac{361}{ \cancel{400}}$

$\sf \implies {45} \times \dfrac{361} {2}$

$\sf \implies \dfrac{16245}{2}$

$\sf \implies 8122.5$

$\sf After \: 3 \: years \: it's \: depreciation \: amount = Rs. \: 8122.5$

$\bf \underline{Now},$

$\sf \implies Depreciation = Principal - Amount$

$\sf \implies Depreciation = 9000 - 8122.5$

$\sf \implies Depreciation = 877.5$

$\bf \underline{Therefore},$

$\sf \implies \underline{\boxed{ \sf Total \: depreciation\:after\: 2\:years =Rs. \: 877.5}}$