document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=959172>Question 959172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tom and Louise wants to establish an account that will supplement their retirement income beginning 30 years from now. Suppose they can invest in a fund that pays 6% interest compounded quarterly. \r<BR>\n" );
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document.write( "a. What is the lump sum they must deposit today so that $500,000 will be available at time of retirement if the account pays?\r<BR>\n" );
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document.write( "b. If they deposit $10,000 in the account now, how long would it take their money to double? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854576 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53937)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Tom and Louise wants to establish an account that will supplement their retirement income beginning 30 years from now. <BR>\n" );
document.write( "Suppose they can invest in a fund that pays 6% interest compounded quarterly.<BR>\n" );
document.write( "a. What is the lump sum they must deposit today so that $500,000 will be available at time of retirement if the account pays?<BR>\n" );
document.write( "b. If they deposit $10,000 in the account now, how long would it take their money to double?<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In his post, @lwsshar3 gave an answer \"about 12 years\" for question (b).\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Actually, this problem admits and assumes a precise (not approximate) answer,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and this precise answer is DIFFERENT from approximate answer by @lwsshar3.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In this my post, I will explain how to get the correct answer.\r<BR>\n" );
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document.write( "b. If they deposit $10,000 in the account now, how long would it take their money to double?<BR>\n" );
document.write( "A/P = 2 = (1+r/n)^nt<BR>\n" );
document.write( "2 = (1.015)^4t<BR>\n" );
document.write( "take log of both sides<BR>\n" );
document.write( "ln(2) = 4t*ln(1.015)<BR>\n" );
document.write( "t = ln(2)/4ln(1.015) ~ 11.6 years  approximately.\r<BR>\n" );
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document.write( "11.6 years is approximately 11 years and 7.2 months.\r<BR>\n" );
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document.write( "This number we should round to 11 years and 9 months, when the bank will make his last compounding<BR>\n" );
document.write( "at the end of the 3rd quarter of the 11th year.\r<BR>\n" );
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document.write( "So, the UNIQUELY correct and precisely accurate answer to the problem's question is 11 years and 9 months.\r<BR>\n" );
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document.write( "It is the time, when the amount at the account first time will get and exceed the doubled value of the principal.\r<BR>\n" );
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document.write( "This problem and the correct answer reveal immediately if a person, who solves the problem, <BR>\n" );
document.write( "does really understand what he/she is doing.\r<BR>\n" );
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document.write( "Solved correctly with complete explanations.\r<BR>\n" );
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document.write( "Do not accept any other answer.\r<BR>\n" );
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document.write( "////////// I n t e r e s t i n g //////////\r<BR>\n" );
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document.write( "Today, May 14, 2026, at about 9:05 pm, I posted this problem to Google Overview Artificial Intelligence.\r<BR>\n" );
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document.write( "It practically reproduced the solution by @lwsshar3, giving the answer \"approximately 11.64 years\".\r<BR>\n" );
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document.write( "It shows that this AI does not understand what he/it is doing<BR>\n" );
document.write( "and teaches visitors in WRONG WAY.\r<BR>\n" );
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document.write( "Ten minutes later, I posted this problem to another AI web-site, www.math-gpt.org/\r<BR>\n" );
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document.write( "It produced the same solution and the same answer as @lwsshar3<BR>\n" );
document.write( "and also demonstrated that it does not understand what it is doing - <BR>\n" );
document.write( "and teaches in WRONG WAY.\r<BR>\n" );
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document.write( "It is how the contemporary AI (plural) work in solving school Math problems:\r<BR>\n" );
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document.write( "it reminds me a railway, where explosive mines are buried in the ground at every 30 meters.\r<BR>\n" );
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document.write( "Obviously, for this class of problems, the base of solutions should be completely replaced  <BR>\n" );
document.write( "and the AIs should be re-trained from scratch.\r<BR>\n" );
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document.write( "It also tells me that those members in AI teams who allowed/(are responsible for) such situation, <BR>\n" );
document.write( "do understand nothing in their job.\r<BR>\n" );
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document.write( "Let the managers of these project consider this my post as an alarm signal:<BR>\n" );
document.write( "something is VERY WRONG in organization of their work process.<BR>\n" );
document.write( "I even know - what precisely: there are wrong people in wrong positions,<BR>\n" );
document.write( "and there is a lack of right people in right positions.<BR>\n" );
document.write( "Also, the mechanism of selecting right people for right positions does not function properly.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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