Declining-Balance Depreciation (Book Value)

Declining balance takes the same fraction off whatever is left each year, so the write-down is large at first and shrinks steadily after. A $20,000 asset at 20% a year goes 20,000, then 16,000, then 12,800, then 10,240, which the closed form $B = C(1-d)^k$ reproduces as $20000 \ imes 0.8^3$. This matches how equipment actually loses value far better than a straight line does, which is why most tax authorities use it. Canada's Capital Cost Allowance system is declining balance throughout.

There is a curiosity built into the mathematics: multiplying by a fraction repeatedly never reaches zero. In theory the asset is worth something forever. Accounting rules paper over this by switching to straight line near the end, or by writing off the remainder once it drops below a threshold. It also means you cannot solve for the rate from a book value of exactly zero, and the solver will tell you so.

The rate is often set from the life rather than measured. "Double declining balance" uses $d = 2/n$, so a ten-year asset is written down 20% a year, which is where the figure in the example above comes from.