document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #853166 by ikleyn(53427) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Alison deposits $500 into a new savings account that earns 5 percent interest compounded annually.
\n" ); document.write( "If Alison makes no additional deposits or withdrawals, how many years will it take for the amount
\n" ); document.write( "in the account to double?
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document.write( "We start from the standard formula for the future value of a compounded account\r\n" );
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document.write( "    FV = .\r\n" );
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document.write( "We write this equation for the doubled future value\r\n" );
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document.write( "    1000 = .\r\n" );
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document.write( "Here 'n' is the unknown number of the years (= number of compounding) to find.\r\n" );
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document.write( "We simplify equation (1) step by step\r\n" );
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document.write( "     = .\r\n" );
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document.write( "    2 = .\r\n" );
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document.write( "Take logarithm of both sides \r\n" );
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document.write( "    log(2) = n*log(1.05).\r\n" );
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document.write( "Express and calculate 'n'\r\n" );
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document.write( "    n =  = 14.21  (approximately).\r\n" );
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document.write( "The number of compounding is an integer number - so, we must round this decimal 14.21\r\n" );
document.write( "to the closest GREATER integer 15 in order for the bank be in position to make the last compounding.\r\n" );
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document.write( "ANSWER.  First time the compounded amount will exceed the doubled principal in 15 years.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The solution/answer in the post by @lynnlo both are incorrect,
\n" ); document.write( "so, ignore his post for the peace in your mind.\r
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I N T E R E S T I N G

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\n" ); document.write( "\n" ); document.write( "I checked today, on December 15, 2025, how Artificial Intelligence, Google AI Overview
\n" ); document.write( "treats this problem.\r
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\n" ); document.write( "\n" ); document.write( "It produces the same answer 14.2 years as in the post by @lynnlo, without any critical analysis,
\n" ); document.write( "i.e., treats the problem INCORRECTLY.\r
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\n" ); document.write( "\n" ); document.write( "I copied all references from the Google AI Overview output they are copy-pasted below.\r
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\n" ); document.write( "\n" ); document.write( "[1] https://www.gauthmath.com/solution/1806082773471301/How-long-will-it-take-money-to-double-itself-if-invested-at-5-compounded-annuall\r
\n" ); document.write( "\n" ); document.write( "[2] https://askfilo.com/user-question-answers-smart-solutions/7-determine-how-long-will-it-take-money-to-double-itself-if-3331353538313435\r
\n" ); document.write( "\n" ); document.write( "[3] https://www.nerdwallet.com/banking/calculators/compound-interest-calculator\r
\n" ); document.write( "\n" ); document.write( "[4] https://study.com/skill/learn/finding-the-final-amount-in-a-word-problem-on-compound-interest-explanation.html\r
\n" ); document.write( "\n" ); document.write( "[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-/\r
\n" ); document.write( "\n" ); document.write( "[6] https://askfilo.com/user-question-answers-smart-solutions/at-what-rate-a-sum-of-money-will-be-doubled-in-20-years-3133353733363230\r
\n" ); document.write( "\n" ); document.write( "[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-/\r
\n" ); document.write( "\n" ); document.write( "[8] https://brainly.in/question/9793176\r
\n" ); document.write( "\n" ); document.write( "[9] https://www.math.uni.edu/~campbell/mdm/cont.html\r
\n" ); document.write( "\n" ); document.write( "[10] https://www.comerica.com/insights/wealth-management/wealth-preservation/financially-fit-clients-do-math.html\r
\n" ); document.write( "\n" ); document.write( "[11] https://www.quora.com/How-long-will-it-take-to-double-your-savings-if-you-earn-5-percent-interest-compounded-annually\r
\n" ); document.write( "\n" ); document.write( "[12] https://prepp.in/question/at-what-percent-of-compound-interest-per-annum-a-s-65e1ec82d5a684356ea12319\r
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\n" ); document.write( "\n" ); document.write( "I checked each and every of these references.\r
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\n" ); document.write( "\n" ); document.write( "Part of them produced the treatment for precisely this posed problem, but all
\n" ); document.write( "produced treatments/answers were incorrect from the point of view of final rounding.\r
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\n" ); document.write( "\n" ); document.write( "Other references were IRRELEVANT to the posed problem, which were especially sad to see.\r
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\n" ); document.write( "\n" ); document.write( "Naturally, I informed Google AI Overview about this their mistake via their feedback system.\r
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\n" ); document.write( "\n" ); document.write( " . . . . . . . . . . . . . . . . . . . . \r
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\n" ); document.write( "\n" ); document.write( "In opposite, another Artificial Intelligence, https://math-gpt.org/, treats the problem IDEALLY (precisely as in my solution).\r
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