document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257689>Question 257689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You deposit $25,000 in an account to accrue interest for 40 years. the account pays 4% compunded anually. Assume that the income tax on the earned interest is 30%. Which of the following plans produces a larger balance after all income tax is paid? <BR>\n" );
document.write( "(A) the income tax on the interest that is earned is paid in one lump sum at the end of 40 years.<BR>\n" );
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document.write( "(B)The income tax on the interest that is earned each year is paid at the end of each year.\r<BR>\n" );
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document.write( "i know i am supposed to use the A=P(1+r/n)^nt equation, but im not sure where to put the information.\r<BR>\n" );
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document.write( "please help. thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189676 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 25000 deposited today for 40 years.<BR>\n" );
document.write( "pays 4% compounded annually.<BR>\n" );
document.write( "income tax on the interest is 30%.\r<BR>\n" );
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document.write( "which of the following earns more?\r<BR>\n" );
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document.write( "(A) the income tax on the interest that is earned is paid in one lump sum at the end of 40 years.\r<BR>\n" );
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document.write( "if you pay the income tax at the end of the 40 years, then you will pay as follows:\r<BR>\n" );
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document.write( "the formula is future worth of a present amount.\r<BR>\n" );
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document.write( "that formula is:\r<BR>\n" );
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document.write( "f = p * (1+r)^n\r<BR>\n" );
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document.write( "f = future value<BR>\n" );
document.write( "p = present amount<BR>\n" );
document.write( "r = 4% per year divided by 100% = .04 interest rate per year.<BR>\n" );
document.write( "n = number of years = 40\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "f = 25000 * (1.04)^40 \r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "f = 120025.51578\r<BR>\n" );
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document.write( "uncle sam takes 30% of the profit and you are left with your original investment plus 70% of the profit.\r<BR>\n" );
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document.write( "120025.51578 - 25000 = 95025.5157 * .7 = 66517.86099 + 25000 = 91517.86099 = $91,517.86\r<BR>\n" );
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document.write( "(B)The income tax on the interest that is earned each year is paid at the end of each year.\r<BR>\n" );
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document.write( "you earn 4% per year and uncle sam takes 30% of that out each year.\r<BR>\n" );
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document.write( "you are netting 4% minus .3 * 4% = 4% minus 1.2% = 2.8% per year.\r<BR>\n" );
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document.write( "that's what you are earning each year after uncle sam takes out his share at the end of each year.\r<BR>\n" );
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document.write( "same formula applies.\r<BR>\n" );
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document.write( "f = p * (1+r)^n \r<BR>\n" );
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document.write( "p = 25000<BR>\n" );
document.write( "r = 2.8% / 100% = .028 interest rate per year.<BR>\n" );
document.write( "n = 40 years.\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "f = 25000 * (1.028)^40\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "f = 75450.92962 = $75,450.93\r<BR>\n" );
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document.write( "you make more money paying uncle sam at the end of the 40 years rather than at the end of each year.\r<BR>\n" );
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document.write( "this is because the money that you would have been paying uncle sam each year is sitting in your account earning more money each year.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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