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12 December, 00:45

2. A savings account is started with an initial deposit of $600. The account earns 2.1 % interest compounded annually.

(a) Write an equation to represent the amount of money in the account as a function of time in years.

(b) Find the amount of time it takes for the account balance to reach $800. Show your work.

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  1. 12 December, 03:02
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    Step-by-step explanation:

    Initial amount that was deposited into the savings account is $600 This means that the principal,

    P = 600

    The account earns 2.1 % interest compounded annually ... This means that it was compounded once in a year. So

    n = 1

    The rate at which the principal was compounded is 2.1%. So

    r = 2.1/100 = 0.021

    It was compounded for t years. So

    t = t

    a) The formula for compound interest is

    A = P (1+r/n) ^nt

    A = total amount in the account at the end of t years. Therefore

    A = 600 (1+0.021/1) ^1*t

    A = 600 (1.021) ^t

    b) when A = $800, it becomes

    800 = 600 (1.021) ^t

    Dividing both sides by 600, it becomes

    1.33 = (1.021) ^t

    Taking the tth root of both sides

    t = 14 years

    It will take 14 years
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