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Answer :
Final answer:
The value of a machine after 5 years of depreciating at a rate of 20% per year is calculated by repeatedly reducing the initial cost by 20% each year. After performing these calculations, the estimated value of the machine at the end of 5 years is rounded to Rs 5,000.
Explanation:
The student in the question is asking how to calculate the value of a machine after 5 years of depreciation at a rate of 20% per annum. To solve this, we use the formula for depreciation which involves reducing the initial value of the machine by 20% each year.
The initial value of the machine is Rs 15,625. To find the value after one year, we calculate 20% of 15,625, which is Rs 3,125, and subtract that from the initial value. The value at the end of year 1 will be Rs 12,500 (15,625 - 3,125). We continue to reduce this new value by 20% each subsequent year for a total of 5 years.
- Year 1: 15625 - (15625 * 0.20) = Rs 12,500
- Year 2: 12500 - (12500 * 0.20) = Rs 10,000
- Year 3: 10000 - (10000 * 0.20) = Rs 8,000
- Year 4: 8000 - (8000 * 0.20) = Rs 6,400
- Year 5: 6400 - (6400 * 0.20) = Rs 5,120
However, the estimated value is given in rounded hundreds, so we round Rs 5,120 to the nearest option which is Rs 5,000 (answer D).
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