engineering economy

Derivation of Formula for Sum of Years Digit Method (SYD)

The depreciation charge and the total depreciation at any time m using the sum-of-the-years-digit method is given by the following formulas:
 

Depreciation Charge:

$d_m = (FC - SV) \dfrac{n - m + 1}{SYD}$

 

Total depreciation at any time m

$D_m = (FC - SV) \dfrac{m(2n - m + 1)}{2 \times SYD}$

 

Where:
FC = first cost
SV = salvage value
n = economic life (in years)
m = any time before n (in years)
SYD = sum of years digit = 1 + 2 + ... + n = n(1 + n)/2
 

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