Depreciation. In business, equipment is often depreciated...

Depreciation. In business, equipment is often depreciated using the double declining-balance method. In this method, a piece of equipment with a life expectancy of $N$ years, costing SC, will depreciate to a value of $\$ V$ in $n$ years, where $n$ is given by the formula $$ n=\frac{\log V-\log C}{\log \left(1-\frac{2}{N}\right)} $$ A computer that cost $\$ 37,000$ has a life expectancy of 5 years. If it has depreciated to a value of $\$ 8,000,$ how old is it?

Depreciation. In business, equipment is often depreciated using the double declining-balance method. In this method, a piece of equipment with a life expectancy of $N$ years, costing SC, will depreciate to a value of $\$ V$ in $n$ years, where $n$ is given by the formula
$$
n=\frac{\log V-\log C}{\log \left(1-\frac{2}{N}\right)}
$$
A computer that cost $\$ 37,000$ has a life expectancy of 5 years. If it has depreciated to a value of $\$ 8,000,$ how old is it?

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Key Concepts

Logarithms in Solving Exponential Equations

Logarithms are employed to solve equations where the unknown variable is an exponent, such as in exponential decay models. When determining the time period it takes for an asset to depreciate to a specified value, logarithmic transformations help in isolating the time variable in the decay formula.

Exponential Decay

Exponential decay describes the process by which the value of an asset decreases at a rate proportional to its current value. In the context of depreciation, this concept is used to model the decline in asset value over time, particularly under methods that factor in decreasing book values.

Depreciation

Depreciation is the process of allocating the cost of a tangible asset over its useful life. It reflects how the value of the asset decreases over time due to wear and tear, usage, or obsolescence, and it plays a crucial role in both accounting and financial planning.

Double Declining Balance Method

The double declining balance method is an accelerated depreciation technique where an asset is depreciated at twice the rate of the straight-line method. This method applies a constant rate to the declining book value of the asset, resulting in higher depreciation expenses in the earlier years of the asset’s life.

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