Intermath | Workshop Support
Write-up 8


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
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