Assume linear depreciation. A manufacturer buys a new...

Assume linear depreciation. A manufacturer buys a new machine costing 120,000 dollars. It is estimated that the machine has a useful lifetime of ten years and a salvage value of 4000 dollars at that time. (a) Find a formula for the value of the machine after $t$ years, where $0 \leq t \leq 10$ (b) Find the value of the machine after eight years.

Assume linear depreciation.
A manufacturer buys a new machine costing 120,000 dollars.
It is estimated that the machine has a useful lifetime of ten years and a salvage value of 4000 dollars at that time.
(a) Find a formula for the value of the machine after $t$ years, where $0 \leq t \leq 10$
(b) Find the value of the machine after eight years.

Key Concepts

Linear Equation in Depreciation

A linear equation in the context of depreciation models the asset's value as a function of time. It typically takes the form V(t) = V0 - (depreciation rate)*t, where V0 is the initial cost, and t is the time elapsed. This formula aids in determining the asset’s value at any specific time during its useful life.

Depreciation Rate

The depreciation rate is the fixed amount by which an asset’s value decreases each period. It is calculated by subtracting the salvage value from the initial cost and then dividing by the useful life, resulting in a constant annual (or periodic) depreciation expense.

Linear Depreciation

Linear depreciation is a method of allocating the cost of an asset evenly across its useful life. In this approach, the asset’s value decreases by the same amount each period, leading to a straight-line decline in value when graphed over time.

Useful Life

Useful life refers to the duration over which an asset is expected to be productive or economically beneficial. This period determines the number of intervals over which depreciation is calculated, influencing the rate at which the asset loses value.

Salvage Value

Salvage value is the estimated residual value of an asset at the end of its useful life. It represents the asset’s worth when it is no longer in use and helps set the floor for depreciation calculations.

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