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23 June, 08:01

To save for a new car, Trafton invested $3,000 in a savings account that earns 4.5% interest, compounded continuously. After four years, he wants to buy a used car for $4,000. How much money will he need to pay in addition to what is in his savings account? (Round your answer to the nearest cent.)

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  1. 23 June, 09:10
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    Answer: he needs an additional $408.3 to buy the car.

    Step-by-step explanation:

    The formula for continuously compounded interest is

    A = P x e (r x t)

    Where

    A represents the future value of the investment after t years.

    P represents the present value or initial amount invested

    r represents the interest rate

    t represents the time in years for which the investment was made.

    From the information given,

    P = $3000

    r = 4.5% = 4.5/100 = 0.045

    t = 4 years

    Therefore,

    A = 3000 x e^ (0.045 x 4)

    A = 3000 x e^ (0.18)

    A = $3591.7

    He wants to buy a used car for $4,000. The additional amount that he needs is

    4000 - 3591.7 = $408.3
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