Precalc growth and decay

Alison deposits $500 into a new savings account that earns 5 percent interest compounded annually. If Alison makes no additional deposits or withdrawals, how many years will it take for the amount in the account to double?

the answer is 15 but i think its 14. please explain.

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  1. Sra is right.

    The "calculator" on that webpage is using this formula
    Amount = Principal(1+i)^n

    we have 1000=500(1.05)^n
    2 = 1.05^n
    take log of both sides
    log2 = log(1.05)^n
    log2 = nlog1.05
    n = log2/log1.05 = 14.2

    after 14 years, your money has not yet doubled, close, but not yet.
    Amount = 500(1.05)^14 = 989.97

    So I guess they are right at 15, since you have to go into the 15th year to double your deposit.

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  2. I don't think so because A = Pe^rt
    1000 = 500e^0.05 * t
    2 = e^(0.05 * t)
    ln2 = 0.05t
    t=ln2 / 0.05
    t= 13.86
    You have to round up so 14 is the correct answer.

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  3. No Dublin, that is for compounded continuously. This problem states anually.

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