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A house and lot valued at $100,000$ is being depreciated over 25 years by the straight line method. After 10 years the book value of the asset is $64,000$. since only the value of the house depreciates, find the assumed value of the land. (Ignore inflation.)

House $=\$ 90,000,$ Land $=\$ 10,000$

Algebra

Chapter 1

Functions and their Applications

Section 3

Applications of Linear Functions

Functions

Oregon State University

McMaster University

Harvey Mudd College

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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using linear or straight line depreciation, we are going to be determining the assumed value of land. In a scenario in which we have a house and lot and only the houses depreciating, we are given the information boxed in at the top, that the house and lot are purchased for $100,000 initially. So at time equals zero. We have an initial value, a total value of the property of $100,000 and it's depreciating over a period of 25 years but were given that when time is equal to 10. So after 10 years, the total value of the property is equal to $64,000. We want to know what the value of the land is, considering that it does not appreciate. So in order to do this, let's figure out exactly by how much it has depreciated. After 10 years to do that, we can take $100,000 minus $64,000 to get a total of $36,000. That being the total depreciation that it's had thus far within its 1st 10 years, let's figure out by dividing that by the number of years which is 10. We can get that it has depreciated by $3600 per year, now taking $3600 because it is our per year depreciation rate, multiplying that by our total depreciation time period which is a 25 year depreciation period, has given we end up getting $90,000. So that means that over the 25 year life of this property, it will have appreciated $90,000. But initially the whole entire property, it was where the 100,000. So that must mean that 90,000 is the value of the house, leaving us with 100,000. Subtracting the value of the house gives us a value of $10,000 for the value of the lot.

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