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 what fraction does the value of the house depreciate the first year?
b. If the house is judged to be worth $85,000, what is the value of the first year’s depreciation?
1/27.5 = .03636 or about 3.6 % per year
85,000/27.5 = $3090.91
To solve this problem, we need to calculate the depreciation rate of the rental house and then use that rate to find the value of the first year's depreciation.
a. To find the depreciation rate, we divide the total depreciation period (27 ½ years) into 1 year:
Depreciation rate = 1 / 27.5
b. Once we have the depreciation rate, we can calculate the value of the first year's depreciation by multiplying the rate by the initial value of the house.
First year's depreciation = Depreciation rate * Initial value
Let's calculate the answers.
a. Fraction of depreciation in the first year:
Depreciation rate = 1 / 27.5
Therefore, the value of the house depreciates by 1/27.5 (or approximately 0.036363636, which can be rounded to 0.036) in the first year.
b. Value of the first year's depreciation:
Given an initial value of $85,000, we can use the depreciation rate to find the value of the first year's depreciation.
First year's depreciation = Depreciation rate * Initial value
First year's depreciation = 0.036 * $85,000
First year's depreciation = $3,060
Therefore, the value of the first year's depreciation is $3,060.