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18 July, 09:10

If Alexis invests $2,000 into a fund that earns 5.5% interest compounded annually, how long will it take for her investment to grow into $100,000?

Group of answer choices

About 62 years

About 58 years

About 73 years

About 108 years

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Answers (1)
  1. 18 July, 12:48
    0
    Answer: About 73 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 = 2000

    r = 5.5% = 5.5/100 = 0.055

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

    A = 100000

    Therefore,.

    100000 = 2000 (1 + 0.055/1) ^1 * t

    100000/2000 = (1.055) ^t

    50 = 1.055^t

    Taking log of both sides, it becomes

    Log 50 = log 1.055^t

    1.699 = t * log 1.055

    1.699 = 0.0234t

    t = 1.699/0.0234

    t = 72.6

    Approximately 73 years
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