# 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. Determine 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?

Result

a =  100000
b2 =  90000
b3 =  81000
c =  348678.44

#### Solution:

$t = 10 \ y \ \\ x = 1000000 \ \\ \ \\ q = 1/t = 1/10 = \dfrac{ 1 }{ 10 } = 0.1 \ \\ a = x \cdot \ q = 1000000 \cdot \ 0.1 = 100000 = 1.000000\cdot 10^{ 5 }$
$b_{ 2 } = q \cdot \ (x - a) = 0.1 \cdot \ (1000000 - 100000) = 90000$
$b_{ 3 } = q \cdot \ (x - a-b_{ 2 }) = 0.1 \cdot \ (1000000 - 100000-90000) = 81000$
$k_{ 10 } = (1-q)^{10} = (1-0.1)^{10} \doteq 0.3487 \ \\ c = k_{ 10 } \cdot \ x = 0.3487 \cdot \ 1000000 = 348678.4401 = 348678.44$

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