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6 November, 17:12

Johnny opened a savings account 3 years ago. The account earns 7% interest, compounded continuously. If the current balance is $200.00, how much did he deposit initially? Round your answer to the nearest cent.

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  1. 6 November, 17:23
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    Answer: the initial deposit is $162.1

    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,

    r = 7% = 7/100 = 0.07

    t = 3 years

    A = $200

    Therefore,

    200 = P x 2.7183^ (0.07 x 3)

    200 = P x 1.234

    P = 200/1.234

    P = $162.1 to the nearest cent
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