An investment of $1,000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed f

Question

An investment of $1,000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1,000 increased to $4,000 by earning interest. In how many years after the initial investment was made would the $1,000 have increased to $8,000 by earning interest at that rate

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Kennedy 2 months 2021-10-09T05:29:55+00:00 1 Answer 0 views 0

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    2021-10-09T05:31:32+00:00

    Answer: it will take 18.4 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 = $1000

    A = $4000

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

    t = 12 years

    Therefore,.

    4000 = 1000(1 + r/1)^1 × 12

    4000/1000 = (1 + r)^12

    4 = (1 + r)^12

    Log 4 = 12 log (1 + r)

    0.602/12 = log (1 + r)

    0.0501 = log (1 + r)

    Taking inverse log of both sides, it becomes

    10^0.0501 = 10^log(1 + r)

    1.122 = 1 + r

    r = 1.122 – 1 = 0.122

    At r = 0.122 and A = 8000

    Therefore,

    8000/1000 = (1 + r)^1 × t

    8 = (1 + 0.122)^t

    8 = (1.122)^t

    Log 8 = tlog 1.122

    0.903 = 0.049 × t = 0.049t

    t = 0.903/0.049

    t = 18.4 years

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