Because of a recession, the value of a new house depreciated 10% each year for 3 yr in a row. Then, for the next 3 yr, the value of the house increased 10% each year. Did the value of the house increase or decrease after 6 yr? Explain.
I feel that the house did not increase at all in the 6 years because the gains in the last 3 years offset the initial losses in the first three years.
What do you think?
After 6 yrs, the house decreased.
The gains do not offset the losses.
After three years the price is down 30% to start with, so the 10% increases are on calculated on a lower value.
Do an example. On $50,000, after 6 years the house is down in value approx. 3%.
Based on your reasoning, it seems that you believe the value of the house did not increase or decrease after 6 years. Let's break down the calculation to see if your reasoning is correct.
In the first three years, the value of the house depreciated by 10% each year. To calculate the value of the house after three years, we need to multiply the original value of the house by 90% three times:
Value after 3 years = Original value × 0.9 × 0.9 × 0.9
Similarly, in the next three years, the value of the house increased by 10% each year. To calculate the value of the house after six years, we need to multiply the value after three years by 110% three times:
Value after 6 years = Value after 3 years × 1.1 × 1.1 × 1.1
Let's simplify these calculations:
Value after 3 years = Original value × 0.9 × 0.9 × 0.9
Value after 6 years = (Original value × 0.9 × 0.9 × 0.9) × 1.1 × 1.1 × 1.1
Now, let's consider a hypothetical example. Let's say the original value of the house is $100,000:
Value after 3 years = $100,000 × 0.9 × 0.9 × 0.9 = $72,900
Value after 6 years = $72,900 × 1.1 × 1.1 × 1.1 ≈ $96,887.79
As we can see from this example, the value of the house increased from $72,900 to approximately $96,887.79 after six years. Therefore, contrary to your belief, the value of the house actually increased over the six-year period.
In conclusion, the value of the house increased after six years, as the gains in the last three years offset the initial losses in the first three years.