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? How can I explain this
Let's look at $1000
after 3 years depreciation of 10%
amount = 1000(.9)^3
Then this appreciates for 3 years at 10%
final amount = 1000(.9)^3 (1.1)^3
= 970.30
So what do you think?
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.
Let's say the initial value of the house is $100.
For the first three years, the value of the house depreciates by 10% each year. To calculate the new value after each year, we need to multiply the previous year's value by 0.9 (1 - 0.1 depreciation rate):
Year 1: $100 x 0.9 = $90
Year 2: $90 x 0.9 = $81
Year 3: $81 x 0.9 = $72.90
After three years of depreciation, the house's value is $72.90.
For the next three years, the value of the house increases by 10% each year. To calculate the new value after each year, we need to multiply the previous year's value by 1.10 (1 + 0.1 growth rate):
Year 4: $72.90 x 1.10 = $80.19
Year 5: $80.19 x 1.10 = $88.21
Year 6: $88.21 x 1.10 = $97.03
After three years of appreciation, the house's value is $97.03.
Comparing the initial value of $100 to the final value of $97.03, we can see that the value of the house has decreased after 6 years.
Therefore, the value of the house has decreased after 6 years due to the combined effect of the three years of depreciation followed by the three years of appreciation during a recession.