Precalc growth and decay

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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.

  • Precalc growth and decay -

    I wonder also how the answer can be 15 years. Go to the following site, with the calculator for figuring out compound interest.

    http://www.1728.com/compint.htm

    Since you want to know how many years it will take:
    1. click on YEARS
    2. Input Principal = 500
    3. Input Total = 1000
    4. Input Rate = 5

    I get: 14.2067!

    Here's another calculator to use: http://www.moneychimp.com/calculator/compound_interest_calculator.htm

    When I used 14 as the number of years = 989.97
    When I used 15 as the number of years = 1039.46

    You were only asked to end up with $1,000.00

    Here's the formula : M = P(1+i)n

    M = final amount including principal
    P = principal amount
    i = rate of interest per year
    n - number of years invested

    Most people use the compound interest calculator! Please check all your numbers carefully.

    Sra

  • Precalc growth and decay -

    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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