The value of a machine depreciates 10% annually. Its present value is ₹ 64,800. Find :

(i) its value after 2 years,

(ii) its value 2 years ago.

(i) Given,

Present value of machine (V) = ₹ 64,800

R = 10%

n = 2 years

By formula,

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

Substituting the values in formula,

$\text{Value of machine after 2 years} = 64800 \times \Big(1 - \dfrac{10}{100}\Big)^2 \\[1em] =64800 \times \Big(\dfrac{100 - 10}{100}\Big)^2 \\[1em] =64800 \times \Big(\dfrac{90}{100}\Big)^2 \\[1em] =64800 \times \Big(\dfrac{9}{10}\Big)^2 \\[1em] =64800 \times \dfrac{81}{100} \\[1em] =\dfrac{64800 \times 81}{100} \\[1em] = ₹ 52,488$

Hence, value of machine after two years = ₹ 52,488.

(ii) Given,

Present value of machine (V) = ₹ 64,800

R = 10%

n = 2 years

By formula,

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

Substituting the values in formula,

$\text{Value of machine 2 years ago } = \dfrac{64800}{\Big(1 - \dfrac{10}{100}\Big)^2} \\[1em] =\dfrac{64800}{\Big(\dfrac{100 - 10}{100}\Big)^2} \\[1em] =\dfrac{64800}{\Big(\dfrac{90}{100}\Big)^2} \\[1em] =\dfrac{64800}{\Big(\dfrac{9}{10}\Big)^2} \\[1em] =\dfrac{64800}{\dfrac{81}{100}} \\[1em] =\dfrac{64800 \times 100}{81} \\[1em] =₹ 80,000$

Hence, value of machine two years ago = ₹ 80,000.