Question

A property's value is $400,000 and its land value is $75,000. Assuming a depreciation term of 39 years, what is the amount of annual depreciation?

Answer 1

Answer
8333 annual dep
Step by step:
Property value=400,000
Land=75000
You have to know that land can't be depreciated, so the depreciation will applied on the value of the property without the value of the land, to do that, substruct the value of the land from the value of the property
400000-75000= 325000
Then cumpute the dep amount
325000÷39 years to get 8333 which is annual dep.

Answer 2

$\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &75000\\ P=\textit{initial amount}\dotfill &400000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &39\\ \end{cases} \\\\\\ 75000=400000(1 - \frac{r}{100})^{39}\implies \cfrac{75000}{400000}=\left( \cfrac{100-r}{100} \right)^{39}$

$\cfrac{3}{16}=\left( \cfrac{100-r}{100} \right)^{39}\implies \sqrt[39]{\cfrac{3}{16}}=\cfrac{100-r}{100}\implies 100\sqrt[39]{\cfrac{3}{16}}=100-r \\\\\\ r=100-100\sqrt[39]{\cfrac{3}{16}}\implies r\approx 4.2$