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30 January, 05:52

A total of $2,000 is invested at an annual interest rate of 2%. Find the balance in the account after

10 years if it is compounded continuously (round to the nearest dollar).

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  1. 30 January, 08:55
    0
    The balance in the account after 10 years is US$ 2,442.81

    Step-by-step explanation:

    1. Let's review the data given to us for answering the question:

    Investment amount = US$ 2,000

    Duration of the investment = 10 years

    Annual interest rate = 2% compounded continuously

    2. Let's find the future value of this investment after 10 years, using the following formula:

    FV = PV * eˣ ⁿ

    PV = Investment = US$ 2,000

    number of periods (n) = 10 (10 years compounded continuously)

    rate (x) = 2% = 0.02

    e = 2.71828 (Euler's number)

    Replacing with the real values, we have:

    FV = 2,000 * (2.71828) ^0.02*10

    FV = 2,000 * 2.71828^0.2

    FV = 2,000 * 1.2214027

    FV = US$ 2,442.81
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