Because of a recession, the value of a new house depreciated 10% each year for three years in a row. Then, for the next three years, the value of the house increased 10% each year. Did the value of the house increase, decrease, or remain the same after 6 years?
it decreased the first three years, then increased the next three years. so basically its like it remained the same
Not quite
Decreasing for 3 years at 10%/yr, the value is now .9^3 = .729
Increasing for 3 years from the reduced value, it is finally worth
.729*1.1^3 = .970
SO, the house lost 3% over the 6 years.
To determine whether the value of the house increased, decreased, or remained the same after 6 years, we need to calculate the net change in value.
From the given information, we know that the value of the house depreciated 10% each year for three years. To calculate the new value after three years of depreciation, we will multiply the original value by (1 - 0.1) three times:
New Value after 3 years = Original Value * (1 - 0.1) * (1 - 0.1) * (1 - 0.1)
Next, we are told that the value of the house increased by 10% each year for the next three years. We can calculate the new value after three years of appreciation by multiplying the value after three years of depreciation by (1 + 0.1) three times:
New Value after 6 years = New Value after 3 years * (1 + 0.1) * (1 + 0.1) * (1 + 0.1)
Now, we can compare the new value after 6 years to the original value. If the new value is greater, it means the value of the house increased. If the new value is smaller, it means the value of the house decreased. And if the new value is the same, it means the value of the house remained the same.
By using this calculation method, we can determine whether the value of the house increased, decreased, or remained the same after 6 years.