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14 December, 04:16

Carrie earned $3673 from a summer job and put it in a savings account that earns 10% interest compounded annually. When Carrie started college, she had $7614 in the account which she used to pay her tuition. How long was the money in the account?

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  1. 14 December, 04:39
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    Step-by-step explanation:

    We would apply the formula for determining compound interest which is expressed as

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

    Where

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

    r represents the interest rate.

    n represents the periodic interval at which it was compounded.

    P represents the principal or initial amount deposited

    From the information given,

    A = 7614

    r = 10% = 10/100 = 0.1

    n = 1 because it was compounded once in a year.

    P = 3673

    Therefore,

    7614 = 3673 (1+0.1/1) ^1 * t

    7614/3673 = 1.01^t

    2.073 = 1.01^t

    Taking log of both sides, it becomes

    Log 2.073 = log 1.01^t

    0.3166 = t * 0.0043

    t = 0.3166/0.0043

    t = 73.3
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