Here's the solution to question 3: a) Define compound depreciation. Compound depreciation is the reduction in the value of an asset over time, where the depreciation for each period is calculated on the reduced value of the asset from the previous period, rather than on its original cost. This means the amount of depreciation decreases each year. b) How much price of the machine is depreciated in first year? Find it. Given: Current price of the machine ($P$) = Rs. 50,000 Depreciation rate ($R$) = 20% annually Step 1: Calculate the depreciation in the first year. $$ \text{Depreciation in 1st year} = P \times \frac{R}{100} $$ $$ \text{Depreciation in 1st year} = 50,000 \times \frac{20}{100} $$ $$ \text{Depreciation in 1st year} = 50,000 \times 0.20 $$ $$ \text{Depreciation in 1st year} = 10,000 $$ The price depreciated in the first year is Rs. 10,000. The final answer is $\boxed{\text{Rs. 10,000}}$. c) Will it be possible to buy that machine at half of its current price after 3 years? Give logic with calculation. Given: Current price of the machine ($P$) = Rs. 50,000 Depreciation rate ($R$) = 20% annually Time ($T$) = 3 years Step 1: Calculate the value of the machine after 3 years using the compound depreciation formula. $$ V_T = P \left(1 - \frac{R}{100}\right)^T $$ $$ V_3 = 50,000 \left(1 - \frac{20}{100}\right)^3 $$ $$ V_3 = 50,000 \left(1 - 0.2\right)^3 $$ $$ V_3 = 50,000 \left(0.8\right)^3 $$ $$ V_3 = 50,000 \times 0.512 $$ $$ V_3 = 25,600 $$ The value of the machine after 3 years is Rs. 25,600. Step 2: Calculate half of its current price. $$ \text{Half of current price} = \frac{50,000}{2} = 25,000 $$ Half of the current price is Rs. 25,000. Step 3: Compare the value after 3 years with half of the current price. Since $V_3 = \text{Rs. } 25,600$ and half of the current price is $\text{Rs. } 25,000$, we have: $$ 25,600 > 25,000 $$ The value of the machine after 3 years (Rs. 25,600) is greater than half of its current price (Rs. 25,000). Conclusion: No, it will not be possible to buy that machine at half of its current price after 3 years. The final answer is $\boxed{\text{No, because the value after 3 years is Rs. 25,600, which is greater than half the current price of Rs. 25,000.}}$.