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24 January, 01:33

How much money, invested at an interest rate of r % per year compounded continuously, will amount to A dollars after t years? (Round your answer to the nearest cent.)

A = 300,000, r = 3.8, t = 18

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  1. 24 January, 03:11
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    Answer: $151377.5 should be invested.

    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.

    e is the mathematical constant approximated as 2.7183.

    From the information given,

    A = $300000

    r = 3.8% = 3.8/100 = 0.038

    t = 18 years

    Therefore,

    300000 = P x 2.7183^ (0.038 x 18)

    300000 = P x 2.7183^ (0.684)

    300000 = 1.9818P

    P = 300000/1.9818

    P = $151377.5
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