Reducing balance method

A company buys an item having a useful life of 10 years for 1,000,000. If the company depreciates the item by the reducing balance method,
a. find the depreciation for the first year.
b. Estimate the depreciation for the second and third years.
c. What is the salvage value of the asset?

Correct answer:

a =  100000
b₂ =  90000
b₃ =  81000
c =  348678.4401

Step-by-step explanation:

$$\begin{gathered} t=10\text{y} \\ x=1000000 \\ q=1/t=1/10=\frac{1}{10}=0.1 \\ a=x\cdot q=1000000\cdot 0.1=100000 \end{gathered}$$

$b_2=q\cdot (x-a)=0.1\cdot (1000000-100000)=90000$

$b_3=q\cdot (x-a-b_2)=0.1\cdot (1000000-100000-90000)=81000$

$$\begin{gathered} k_{10}=(1-q{)}^{10}=(1-0.1{)}^{10}\doteq 0.3487 \\ c=k_{10}\cdot x=0.3487\cdot 1000000=348678.4401\doteq 3.487\cdot 10^5 \end{gathered}$$

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