Because of a recession, the value of a new house depreciated 10% each year for 3 years in a row. Then, for the next 3 years, the value of the house increased 10% each year. Had the value of the house increased or decreased after 6 years? Explain please!!
the original value does not matter
e.g. let's start with 100,000
after 3 years:
value = 100,000(.9)^3
after 3 more years:
value = 100,000(.9)^3 (1.1)^3
= 97,029.9
so what do you think?
Here is a new question for you.
Would it matter if the value first increased by 10% for the first 3 years, and then decreased by 10% for the next 3 years ?
I am 100% confused on this.
To determine whether the value of the house increased or decreased after 6 years, we need to calculate the overall change in value.
Let's start by assuming the original value of the house is $100.
During the recession, the value of the house depreciated by 10% each year for 3 years. To calculate the depreciation, we multiply the original value by (1 - depreciation rate).
After the first year, the value would be $100 * (1 - 0.10) = $90.
After the second year, the value would be $90 * (1 - 0.10) = $81.
After the third year, the value would be $81 * (1 - 0.10) = $72.90.
Next, we consider the following three years when the value of the house increased by 10% each year. To calculate the appreciation, we multiply the current value by (1 + appreciation rate).
After the fourth year, the value would be $72.90 * (1 + 0.10) = $80.19.
After the fifth year, the value would be $80.19 * (1 + 0.10) = $88.21.
After the sixth year, the value would be $88.21 * (1 + 0.10) = $96.63.
So, after 6 years, the value of the house increased from its original value of $100 to $96.63. Therefore, the value of the house decreased.