Depreciate 6413

The company bought a new machine for CZK 350,000. Due to wear and tear, its price will decrease by 10% annually. The machine can be written off if its price drops below 30% due to wear and tear. Determine how many years the company can depreciate the machine.

Correct answer:

n =  12

Step-by-step explanation:

$$\begin{gathered} q=1-\frac{10}{100}=\frac{1\cdot 100}{100}-\frac{10}{100}=\frac{100}{100}-\frac{10}{100}=\frac{100-10}{100}=\frac{90}{100}=\frac{9}{10}=0.9 \\ {q}^n=0.30 \\ n\ln q=\ln 0.30 \\ {n}_1=\ln 0.30/\ln q=\ln 0.30/\ln 0.9\doteq 11.4272 \\ n=\lceil n_1\rceil =\lceil 11.4272\rceil =12 \end{gathered}$$

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