## Matt purchased a new car for $30,000. The car depreciates approximately 12% of its value each year compounded continuously.. How much is it

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## Answers ( )

Answer:It is worth

$54,664after 5 yearsStep-by-step explanation:Compound continuous interest can be calculated using the formula:

∵ Matt purchased a new car for $30,000

∴

P = 30,000∵ The car depreciates approximately 12% of its value each year

compounded continuously

∴ r = 12%

– Change it to decimal by divide it by 100

∴

r= 12 ÷ 100= 0.12∵

t = 5 years– Substitute all of these values in the formula above

∴

∴

∴ A = 54663.56401 dollars

– Round it to the nearest dollar

∴ A = 54,664 dollars

It is worth $54,664 after 5 years