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4 July, 02:44

Stella invested $42,000 in an account paying an interest rate of 4 7/8% compounded quarterly. Chloe invested $42,000 in an account paying an interest rate of 4 1/2% compounded annually. To the nearest dollar, how much money would Stella have in her account when Chloe's money has tripled in value?

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  1. 4 July, 04:47
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    Answer: Stella would have $15036 more than Chloe.

    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

    Considering Chloe's investment,

    P = 42000

    r = 4.5% = 4.5/100 = 0.045

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

    A = 42000 * 3 = 126000

    Therefore,.

    126000 = 42000 (1 + 0.045/1) ^1 * t

    126000/42000 = (1.045) ^t

    3 = (1.045) ^t

    Taking log of both side,

    Log3 = tlog1.045

    0.4771 = 0.019t

    t = 0.4771/0.019

    t = 25.11

    Approximately 25 years

    Considering Stella's investment,

    t = 25

    P = 42000

    r = 4.875% = 4.875/100 = 0.04875

    n = 4 because it was compounded 4 times in a year.

    Therefore,

    A = 42000 (1 + 0.04875/4) ^4 * 25

    A = 42000 (1 + 0.0121875) ^100

    A = 42000 (1.0121875) ^100

    A = 42000 * 3.358

    A = $141036

    The difference in amount would be

    141036 - 126000 = $15036
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