Amit started a shop by investing ₹ 5,00,000. In the first year, he incurred a loss of 5%. However, during the second year, he earned a profit of 10% which in the third year rose to 12%. Calculate his net profit for the entire period of three years.

Given,

P = ₹ 5,00,000

r₁ = 5%

r₂ = 10%

r₃ = 12%

Given,

In the first year, Amit incurred a loss of 5%, in second year, he earned a profit of 10% which in the third year rose to 12%.

Substituting the values in formula,

$\text{Value after 3 years} = 500000 \times \Big(1 - \dfrac{5}{100}\Big) \times \Big(1 + \dfrac{10}{100}\Big) \times \Big(1 + \dfrac{12}{100}\Big) \\[1em] = 500000 \times \Big(\dfrac{100 - 5}{100}\Big) \times \Big(\dfrac{100 + 10}{100}\Big) \times \Big(\dfrac{100 + 12}{100}\Big) \\[1em] = 500000 \times \Big(\dfrac{95}{100}\Big) \times \Big(\dfrac{110}{100}\Big) \times \Big(\dfrac{112}{100}\Big) \\[1em] = 500000 \times \Big(\dfrac{19}{20}\Big) \times \Big(\dfrac{11}{10}\Big) \times \Big(\dfrac{28}{25}\Big) \\[1em] = \dfrac{500000 \times 19 \times 11 \times 28}{20 \times 10 \times 25} \\[1em] = ₹ 5,85,200$

Net profit = Value after 3 years - Investment

= ₹ 5,85,200 - ₹ 5,00,000

= ₹ 85,200

Hence, the net profit for the entire period of three years = ₹ 85,200.