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Xavier is going to invest $3,900 and leave it in an account for 14 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Xavier to end up with $9,200

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  1. Today, 00:08
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    Answer: the interest rate is 6%

    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,

    P = $3900

    A = $9200

    t = 14 years

    n = 365 because it was compounded 365 times in a year.

    Therefore,

    9200 = 3900 (1 + r/365) ^365 * 14

    9200/3900 = (1 + 0.0027274r) ^5110

    2.359 = (1.0027274r) ^5110

    Taking log of both sides of the equation, it becomes

    Log 2.359 = 5110 log (1 + 0.0027274r)

    0.373 = 5110 log (1 + 0.0027274r)

    0.373/5110 = log (1 + 0.0027274r)

    0.000073 = log (1 + 0.0027274r)

    Taking inverse log of both sides of the equation, it becomes

    10^0.000073 = 10^log (1 + 0.0027274r)

    1.000168 = 1 + 0.0027274r

    0.0027274r = 1.000168 - 1

    0.0027274r = 0.000168

    r = 0.000168/0.0027274

    r = 0.06

    r = 0.06 * 100 = 6%
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