Huge Math Word Problem
posted by Anonymous .
The owner of a
rental house can depreciate its value over a period of 27 1/2
years, meaning that the value of the house declines
at an even rate over that period of time until the value
is $0.
My question is by what fraction would the value of the house depreciate the first year and
If the house is judged at 85,000, what is the value of the first year's depreciation?

If you want the house to depreciate to zero, there has to be a writeoff value below which the house is deemed to be zero.
Mathematically, at a constant rate of depreciation, even at 10% per year, we will never get rid of the value of the house, even in a hundred years, because there is always 90% of what's left from last year.
If you draw the graph of the value of the house against time, the value decreases gradually but very slowly towards, but never quite, zero.
The xaxis (where y=0) is called a horizontal asymptote. 
Wow, then why was that even asked as a problem?
Also, what about the second part of my question? If the house is judged at 85,000, what is the value of the first year's depreciation? 
It depends on the rate of depreciation, which means that if an answer is not found for the first part, the second part cannot be answered.
Try this:
If the house depreciates at 10% a year, every year the value of the house is 0.9 of the previous year's value.
After 100 years, the value of the house is
85000*0.9^{100}
=$2.26
Still not quite zero.
The key is the word "even rate". If your teacher interpretes it differently, for example, the same amount every year, then it can go down to zero after a certain number of years. But it says "rate", which is a proportion.
Sorry, I cannot go further than this. Perhaps someone else may have other ideas. 
I understand. Thank you so much.

I just reread the question again and it seems to me more a taxrelated problem than math related problem.
This may mean that the depreciation permitted (by the IRS) is uniformly 1/27.5 of its present value every year.
So the annual depreciation (fixed) amount is 85000/27.5= is 3091 and after 27.5 years, the rental house has no more residual value.
During this period, the owner can claim $3091 every year as part of the investment expenses, and so this amount will be considered deductible from taxable income from other sources. However, his will have to pay dearly at the end when he sells the house, because the full sale price will be or can be considered capital gains, and so taxable.
It's always the same saying, you pay now, or you pay later!
So to make a long story short, if my interpretation is correct, then the fraction of the cost is 1/27.5 for the first year, and the first (and subsequent) year amount is $3091.
Respond to this Question
Similar Questions

finance
can anyone help me set up this problem bc im totally lost.... if a house = $125,000 you want to buy this house in 10 years its expected to increase 5% a year over a 10 year period assuming you can earn 10% annually on investment. how … 
math word problem
The owner of a rental house can depreciate its value over a period of 27 1/2 years, meaning that the value of the house declines at an even rate over that period of time until the value is $0 a. By what fraction does the value of the … 
Math156
I can understand in my head how to solve it I can't figure it out on paper. Help......I'm sure this will be easy for someone. The Rental Depreciation Problem. The owner of a rental house can depreciate its value over a period of years, … 
math
I can understand in my head how to solve it I can't figure it out on paper. Help......I'm sure this will be easy for someone. The Rental Depreciation Problem. The owner of a rental house can depreciate its value over a period of years, … 
math
The Rental Depreciation Problem. The owner of a rental house can depreciate its value over a period of 27 ½ years, meaning that the value of the house declines at an even rate over that period of time until the value is $0. a. By … 
math
Use any problem solving strategy to solve the following problem.The value of a house is expected to increase from its current value of $50,000 by 3%each year .What will the value of the house be after 3 years ? 
Math
You want to make an investment in a continuously compounding account over a period of 100 years. What interest rate is required for your investment to double in that time period? 
Math
You want to make an investment in a continuouslycompounding account over a period of three years. What interest rate is required for your investment to double in that time period? 
Math College 115
You spend $1000 on a computer and for tax purposes chose to depreciate it (or assume it decreases in value) to $0 at a constant rate over a 4year period. a) calculate the rate of chage of the assumed value of the equipment over 4 … 
College Algebra
You spend $1000 on a computer and for tax purposes chose to depreciate it (or assume it decreases in value) to $0 at a constant rate over a 4year period. a) calculate the rate of chage of the assumed value of the equipment over 4 …