*Predicting the Value of a House*
*Problem Statement*
The Miller's house is valued at $80,000. Suppose that the value
increases by 5 percent each year. How much will the house be worth in
thirty years? In *n* years?
*Problem setup*
Determine the value of the Miller's house in
30 years when the value increases by 5% each year. How can you
determine the value of the Miller's house in *n* years?
*Plans to
Solve/Investigate the Problem*
My initial plan is to setup an Excel
spreadsheet to find the value of the Miller's home in 30 years.
*
Investigation/Exploration of the Problem*
As planned, I set up an Excel spreadsheet to
determine the value of the Miller's home in 30 years.
Click here to view spreadsheet. To
establish this spreadsheet I used a formula that calculated 5% of
the value of the Miller's home at year 0 and added this to the original
value for year 1 [$80,000 + $80,000(0.05)]. I repeated this
process and discovered that the Miller's home will have a value of
$354,755.40 in 30 years.
To determine the value of the Miller's home
in *n* years, we can re-write the original formula as:
[$80,000 + $80,000(0.05)] = $84,000
as
$80,000(1.05) = $84,000 which is at
year
n=1.
To continue to the next year we can continue
with:
$84,000(1.05) = $80,000(1.05)(1.05)
= $80,000(1.05)^{2 }= $88,200 which is at year
n=2.
Keep going:
$88,200(1.05) =
$80,000(1.05)(1.05)(1.05) = $80,000(1.05)^{3 }= $92,610 which is
at year
n=3.
The pattern we see:
The value of the Miller's home in *n*
years = $80,000(1.05)^{n}
Play around with this
spreadsheet to see what happens.
*
Author & Contact*
Teresa Johnson
Email me |