A machine depreciates each year at 8% of its value in the beginning of the year. If its value be ₹ 57,500 at the end of the year 2015, find :

(i) its value at the end of the year 2014,

(ii) its value at the end of the year 2016.

(i) Given,

Value of machine at the end of the year 2015 (V) = ₹ 57,500

R = 8%

n = 1 year

By formula,

Value of machine n years ago = ₹ $\dfrac{V}{\Big(1 - \dfrac{r}{100}\Big)^n}$

Substituting the values in formula,

$\text{Value of machine at the end of the year 2014 }=\dfrac{57500}{\Big(1 - \dfrac{8}{100}\Big)^1} \\[1em] =\dfrac{57500}{\dfrac{100 - 8}{100}} \\[1em] =\dfrac{57500}{\dfrac{92}{100}} \\[1em] =\dfrac{57500}{\dfrac{23}{25}} \\[1em] =\dfrac{57500 \times 25}{23} \\[1em] =₹ 62,500$

Hence, value of machine at the end of the year 2014 = ₹ 62,500.

(ii) Given,

Value of machine at the end of the year 2015 (V) = ₹ 57,500

R = 8%

n = 1 year

By formula,

Value of machine after n years = $\Big[V \times \Big(1 - \dfrac{r}{100}\Big)^n \Big]$

Substituting the values in formula,

$\text{Value of machine at the end of 2016}=57500 \times \Big(1 - \dfrac{8}{100}\Big)^1 \\[1em] =57500 \times \Big(\dfrac{100 - 8}{100}\Big) \\[1em] =57500 \times \Big(\dfrac{92}{100}\Big) \\[1em] =57500 \times \dfrac{23}{25} \\[1em] =\dfrac{57500 \times 23}{25} \\[1em] =₹ 52,900.$

Hence, value of machine at the end of the year 2016 = ₹ 52,900.