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

Question

Matt purchased a new car for \$30,000. The car depreciates approximately 12% of its value each year compounded continuously.. How much is it worth after 5 years? Round the answer to nearest dollar.

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2 weeks 2021-10-04T01:15:26+00:00 1 Answer 0

It is worth \$54,664 after 5 years

Step-by-step explanation:

Compound continuous interest can be calculated using the formula: • A is the future value of the investment, including interest
• P is the principal investment amount (the initial amount)
• r is the interest rate in decimal
• t is the time the money is invested for

∵ 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