The cost of a plot is ₹6,40,000. It increases at a rate of 5% of its previous value after every year. What will be its value after two years?
Understand the Problem
The question is asking us to calculate the value of a plot of land after two years, given its initial cost and the annual percentage increase.
Answer
₹ 7,05,600
Answer for screen readers
The value of the plot after two years will be ₹ 7,05,600.
Steps to Solve
- Calculate the increase in value after the first year
The plot increases by 5% of its initial value which is ₹ 6,40,000. So, we calculate 5% of ₹ 6,40,000
$Increase = 5% \times 6,40,000 = \frac{5}{100} \times 6,40,000 = 32,000$
- Calculate the value of the plot after the first year
We add the increase to the initial cost.
$Value_{year1} = Initial,Cost + Increase = 6,40,000 + 32,000 = 6,72,000$
- Calculate the increase in value after the second year
The plot increases by 5% of its value at the end of the first year, which is ₹ 6,72,000. So, we calculate 5% of ₹ 6,72,000
$Increase = 5% \times 6,72,000 = \frac{5}{100} \times 6,72,000 = 33,600$
- Calculate the value of the plot after the second year
We add the increase to the value at the end of the first year.
$Value_{year2} = Value_{year1} + Increase = 6,72,000 + 33,600 = 7,05,600$
The value of the plot after two years will be ₹ 7,05,600.
More Information
The value of the plot increases each year due to a fixed percentage increase, compounding the value.
Tips
A common mistake is to calculate the increase only based on the initial value for both years, without considering the compounding effect. Another mistake would be miscalculating the percentage increase.
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