A piece of property increased in value by 14% in one year and by 10% in the next year. What was the percent of increase over two years?
Let x = original value.
x + .14x + .1(1.14x) = ?
457
To find the percent of increase over two years, we can add the percent increases for each year and calculate the total increase.
First, let's find the increase in value for the first year. If the property increased in value by 14%, we can calculate the new value after the first year by adding 14% of the original value to the original value:
New Value after the first year = Original Value + (14% × Original Value)
= Original Value + (0.14 × Original Value)
= Original Value × (1 + 0.14)
= Original Value × 1.14
Now, let's find the increase in value for the second year. We can calculate the new value after the second year by adding 10% of the value from the first year to the value from the first year:
New Value after the second year = Value after the first year + (10% × Value after the first year)
= Value after the first year + (0.10 × Value after the first year)
= Value after the first year × (1 + 0.10)
= (Original Value × 1.14) × 1.10
Finally, let's calculate the overall increase over two years. We can find this percentage increase by subtracting the original value from the new value after two years, dividing the result by the original value, and multiplying by 100 to get the percentage:
Percent Increase over two years = ((New Value after two years - Original Value) / Original Value) × 100
= (((Original Value × 1.14) × 1.10) - Original Value) / Original Value) × 100
= ((((Original Value × 1.14) × 1.10) / Original Value) - 1) × 100
= (((1.254 × Original Value) / Original Value) - 1) × 100
= 0.254 × 100
= 25.4%
Therefore, the percent of increase over two years is 25.4%.