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28 June, 15:28

If Siddiq invests $10,000 into a fund that earns 8% interest compounded annually, how long will it take for his investment to grow into $100,000?

About 25 years

About 30 years

About 40 years

About 35 years

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  1. 28 June, 15:42
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    Answer: About 30 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 = 10000

    r = 8% = 8/100 = 0.08

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

    A = 100000

    Therefore,

    100000 = 10000 (1+0.08/1) ^1 * t

    100000/10000 = (1.08) ^t

    10 = (1.08) ^t

    Taking log to base 10 of both sides, it becomes

    Log 10 = log 1.08^t

    1 = t * log 1.08 = 0.03342t

    t = 1/0.03342

    t = 29.9

    Approximately 30 years
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