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Question 729539: 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?
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176)   (Show Source):
You can put this solution on YOUR website! FOR THE AMOUT TO DOUBLE IT WILL TAKE 14.2YEARS
TO DOUBLE FROM $500.00 TO$999.67
WHEN YOU ROUND OVER THE .67 IT WILL DOUBLE FROM 500 TO 1000
Answer by ikleyn(53427)  (Show Source):
You can put this solution on YOUR website! .
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?
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We start from the standard formula for the future value of a compounded account
FV =  .
We write this equation for the doubled future value
1000 =  .
Here 'n' is the unknown number of the years (= number of compounding) to find.
We simplify equation (1) step by step
 =  .
2 = .
Take logarithm of both sides
log(2) = n*log(1.05).
Express and calculate 'n'
n =  = 14.21 (approximately).
The number of compounding is an integer number - so, we must round this decimal 14.21
to the closest GREATER integer 15 in order for the bank be in position to make the last compounding.
ANSWER. First time the compounded amount will exceed the doubled principal in 15 years.
Solved.
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The solution/answer in the post by @lynnlo both are incorrect,
so, ignore his post for the peace in your mind.
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I N T E R E S T I N G
I checked today, on December 15, 2025, how Artificial Intelligence, Google AI Overview
treats this problem.
It produces the same answer 14.2 years as in the post by @lynnlo, without any critical analysis,
i.e., treats the problem INCORRECTLY.
I copied all references from the Google AI Overview output they are copy-pasted below.
[1] https://www.gauthmath.com/solution/1806082773471301/How-long-will-it-take-money-to-double-itself-if-invested-at-5-compounded-annuall
[2] https://askfilo.com/user-question-answers-smart-solutions/7-determine-how-long-will-it-take-money-to-double-itself-if-3331353538313435
[3] https://www.nerdwallet.com/banking/calculators/compound-interest-calculator
[4] https://study.com/skill/learn/finding-the-final-amount-in-a-word-problem-on-compound-interest-explanation.html
[5] https://www.vaia.com/en-us/textbooks/math/excursions-in-modern-mathematics-8-edition/chapter-10/problem-27-find-the-apr-of-a-bond-that-doubles-its-value-in-/
[6] https://askfilo.com/user-question-answers-smart-solutions/at-what-rate-a-sum-of-money-will-be-doubled-in-20-years-3133353733363230
[7] https://www.vaia.com/en-us/textbooks/math/contemporary-precalculus-5-edition/chapter-5/problem-75-you-have-5-grams-of-carbon-14-whose-half-life-is-/
[8] https://brainly.in/question/9793176
[9] https://www.math.uni.edu/~campbell/mdm/cont.html
[10] https://www.comerica.com/insights/wealth-management/wealth-preservation/financially-fit-clients-do-math.html
[11] https://www.quora.com/How-long-will-it-take-to-double-your-savings-if-you-earn-5-percent-interest-compounded-annually
[12] https://prepp.in/question/at-what-percent-of-compound-interest-per-annum-a-s-65e1ec82d5a684356ea12319
I checked each and every of these references.
Part of them produced the treatment for precisely this posed problem, but all
produced treatments/answers were incorrect from the point of view of final rounding.
Other references were IRRELEVANT to the posed problem, which were especially sad to see.
Naturally, I informed Google AI Overview about this their mistake via their feedback system.
. . . . . . . . . . . . . . . . . . . .
In opposite, another Artificial Intelligence, https://math-gpt.org/, treats the problem IDEALLY (precisely as in my solution).
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