Rahul purchased a Maruti van for Rs. 1, 96,000 and the rate of depreciation is $$14\frac{2}{7}\% $$  per annum. Find the value of the van after two years.

Solution (By Examveda Team)

$$\eqalign{ & {\text{Value}}\,{\text{of}}\,{\text{maruti}}\,{\text{Van}},\, \cr & {V_0} = Rs.\,196000 \cr & {\text{Rate}}\,{\text{of}}\,{\text{depreciation}},\, \cr & r = 14 {\frac{2}{7}} \% = \frac{{100}}{7}\% ; \cr & {\text{Time}},\,t = 2\,{\text{years}} \cr & {\text{Let}}\,{V_1}\,{\text{is}}\,{\text{the}}\,{\text{value}}\,{\text{after}}\,{\text{depreciation}}. \cr & {V_1} = {V_0} \times {\left[ {1 - \left( {\frac{r}{{100}}} \right)} \right]^t} \cr & {V_1} = 196000 \times {\left[ {1 - \left( {\frac{{\left( {\frac{{100}}{7}} \right)}}{{100}}} \right)} \right]^2} \cr & {V_1} = 196000 \times {\left( {1 - {\frac{1}{7}}} \right)^2} \cr & {V_1} = 196000 \times {\left( {\frac{7-1}{7}} \right)^2} \cr & {V_1} = 196000 \times {\left( {\frac{6}{7}} \right)^2} \cr & {V_1} = \frac{{\left( {196000 \times 36} \right)}}{{49}} \cr & {V_1} = Rs.\,144000 \cr} $$