For tax and accounting purposes, corporations depreciate the value of equipment each year. One method used is called "linear depreciation," where the value decreases over time in a linear manner. Suppose that two years after purchase, an industrial milling machine is worth $780,000, and five years after purchase, the machine is worth $390,000. Find a formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase.

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Business

Lambert

Today, 04:32

For tax and accounting purposes, corporations depreciate the value of equipment each year. One method used is called "linear depreciation," where the value decreases over time in a linear manner. Suppose that two years after purchase, an industrial milling machine is worth $780,000, and five years after purchase, the machine is worth $390,000. Find a formula for the machine value V (in thousands of dollars) at time t ≥ 0 after purchase.

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Angela Rasmussen · Answer 1

Answer: V = ((780000-390000) / 3) x 2) + 780000 = 1040000.

Explanation:

0 1 2 3 4 5

780000 390000

If we know that two years after the purchase, an industrial mill is worth $ 780,000, and five years after the purchase, the machine is worth $ 390,000.

780000 - 390000 = 390000 depreciation contained in periods 3.4 5.

Since the depreciation is linear, 390000/3 = 130000 is the depreciation contained in each of those 3 periods. And it will be the one contained in the first two periods.

If two years after the purchase the industrial mill is worth 780000.

780000 + 130000x2 = 1040000.

The formula is summarized in:

V = ((780000-390000) / 3) x 2) + 780000 = 1040000.