# How to Calculate a Diminishing Installment Rate

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A diminishing installment rate is a mathematical percentage that is used for accounting purposes to depreciate an asset value on a declining basis over the estimated life of that asset. As opposed to a straight-line or equal installment method, the depreciation expenses are higher earlier in the life of the asset, but reduce as the asset ages and higher maintenance costs can be expected to be incurred. The combined total expense of depreciation and maintenance tends to even out over the asset’s life, thus minimizing swings in profit and loss statements.

Identify the following values related to the specific asset for which the rate is being calculated: original cost; salvage or residual value (the cash value of the asset at the end of its useful life in terms of scrap or resale prices); and expected life (number of years the asset can be expected to remain useful). Salvage values and life expectancies are estimated based on either your historical experience with similar assets or other reputable sources such as Kelley Blue Book Values for vehicles. Example: a truck is purchased for \$20,000, you plan to use it for 10 years and, based on previous similar trucks you have owned, it should be worth \$1,000 at the end of that life on the resale or scrap market.

Divide salvage value by the original cost to arrive at the base value (B). Divide 1 by the expected life to arrive at the exponent (E). Use the exponent function of a calculator to multiply the base value by the exponent (mathematically stated as B^E), arriving at the inverse of the installment rate (I). Subtract the inverse from 1 (mathematically written as 1-I). The resulting value is the diminishing installment rate. Continuing the truck example, the following calculations will be made: \$1,000 divided by \$20,000 equals .05; 1 divided by 10 years equals .10; .05 raised to the power of .05 (mathematically written as .05^.1) equals .741; 1 minus .741 equals .259, or 25.9 percent, the diminishing installment rate.

Calculate annual depreciation expense, or the diminishing installment dollar amount, by first identifying net book value, which is original cost less all depreciation accumulated in prior years on that asset. Our truck's net book value in the first year is the original cost of \$20,000 because no depreciation has accumulated at this point. Multiply net book value by the diminishing installment rate to arrive at the current year's depreciation expense. In the first year, the truck’s depreciation expense is \$20,000 times the diminishing installment rate, 25.9 percent, which equals \$5,180. The second year, depreciation expense is \$20,000 minus previous year's depreciation of \$5,180, or \$14,820, times 25.9 percent, which equals \$3,838. Each year, depreciation expense is reduced until the 10th year, or the final year of estimated useful life, when the asset will have depreciated to the estimated salvage value of \$1,000.

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• This depreciation method is known by a variety of other descriptions including declining balance method, written-down method, diminishing balance method and reducing installment method.