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

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    2021-10-04T01:16:58+00:00

    Answer:

    It is worth $54,664 after 5 years

    Step-by-step explanation:

    Compound continuous interest can be calculated using the formula:

    A=Pe^{rt}  

    • 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=(30,000)e^{(0.12)(5)}

    A=(30,000)e^{0.6}

    ∴ A = 54663.56401 dollars

    – Round it to the nearest dollar

    ∴ A = 54,664 dollars

    It is worth $54,664 after 5 years

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