A refrigerator was purchased one year ago for ₹ 20,000. Its value depreciates at the rate of 15% per annum. Find:

(i) its present value,

(ii) its value after 1 year.

(i) Given,

V = ₹ 20,000

R = 15%

n = 1 year

By formula,

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

Substituting the values in formula,

$\text{Present value }=20000 \times \Big(1 - \dfrac{15}{100}\Big)^1 \\[1em] =20000 \times \Big(\dfrac{100 - 15}{100}\Big) \\[1em] =20000 \times \Big(\dfrac{85}{100}\Big) \\[1em] =20000 \times \dfrac{17}{20} \\[1em] =\dfrac{20000 \times 17}{20} \\[1em] = ₹ 17,000$

Hence, present value of refrigerator = ₹ 17,000.

(ii) Given,

V = ₹ 17,000

R = 15%

n = 1 year

By formula,

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

Substituting the values in formula,

$\text{Value after 1 year }=17000 \times \Big(1 - \dfrac{15}{100}\Big)^1 \\[1em] =17000 \times \Big(\dfrac{100 - 15}{100}\Big) \\[1em] =17000 \times \Big(\dfrac{85}{100}\Big) \\[1em] =17000 \times \dfrac{17}{20} \\[1em] =\dfrac{17000 \times 17}{20} \\[1em] =₹ 14,450$

Hence, value of refrigerator after 1 year = ₹ 14,450.