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15 October, 22:57

You deposited $800 into an account paying 4.5% interest compounded continuously. A. How much would be in the account in 5 years? B. How long would it take to double your money?

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  1. 15 October, 23:17
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    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.

    A) From the information given,

    P = $800

    r = 4.5% = 4.5/100 = 0.045

    t = 5 years

    Therefore,

    A = 800 x e^ (0.045 x 5)

    A = 800 x e^ (0.225)

    A = $1002

    B) For it to double,

    A = 2 * 800 = 1600

    Therefore,

    1600 = 800 x e^ (0.045 x t)

    1600/800 = e^ (0.045t)

    2 = e^ (0.045t)

    Taking ln of both sides, it becomes

    Ln2 = 0.045t

    0.693 = 0.045t

    t = 0.693/0.045

    t = 15.4 years
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