Rae deposit 6,000 into a savings account with an interest rate of 4% compounded monthly. how long will it take for the account to be worth 1

Question

Rae deposit 6,000 into a savings account with an interest rate of 4% compounded monthly. how long will it take for the account to be worth 10,000?

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Savannah 1 month 2021-09-11T10:55:29+00:00 1 Answer 0

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    2021-09-11T10:56:58+00:00

    Answer: it will take 13.3 years

    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 = 6000

    A = 10000

    r = 4% = 4/100 = 0.04

    n = 12 because it was compounded 12 times in a year.

    Therefore,.

    10000 = 6000(1 + 0.04/12)^12 × t

    10000/6000(1 + 0.0033)^12t

    1.67 = 1.0033^12t

    Taking log to base 10 of both sides, it becomes

    Log 1.67 = 12tLog 1.0033

    0.223 = 12t × 0.0014

    0.223 = 0.0168t

    t = 0.223/0.0168

    t = 13.3 years

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