Hello, Jeff,
The question wants an equation that describes the value of the house as a funtion of time. Let's pick variable names and units for what we're interested in:
Let y(x) be the value of the house, in $, as a function of time, x, in years. We want an expression that will tell us the value of the house in x years.
We know that for x = 0, the value of the house, y(0), is $140,000. When x = 1, the house value decreases by 13.3%, so we have y(1) = $140,000 - 0.133*(140,000).
I'll rewrite this as: y(1) = ($140,000)(1 - 0.133)
For year 2, y(2), I hope to have sold the home and cut my losses. But in the spirit of math, the new value would be calculated by reducing the first year value by another 13.3%:
y(2) = y(1)*(1 - 0.133)
Substitute the full expression for y(1) to get:
y(2) = ($140,000)(1 - 0.133)(1 - 0.133)
Now we can consolidate the two (1 - 0.133) terms:
y(2) = ($140,000)(1 - 0.133)2
This takes the reduced amount from the end of the first year and reduces it by another 13.3%. Now we can see a trend. The factor (1 - 0.133) is raised to the same number as the year.
y(3) = ($140,000)(1 - 0.133)3
We can generalize this by stating y(n) = ($140,000)(1 - 0.133)n
When n = 10, our home has gone down to a value of $33,589. I suggest a different investment.
Bob
