document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168942>Question 1168942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a person retires 20 years from now. he wants to leave 10000 every month for 10 years after retirement the money then would be 8% compounded monthly. he has invested 50000 in a fixed deposit which pays 10% compounded quartile.how much amount at the end of every six months should he save in bank, which pays 7% compounded semi-annually.(Answers=PV of annuity=824214.81, Amount=360478.40, FV of annuity=463736.41, R=1790.011) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793609 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=793609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's what's happening.\r<BR>\n" );
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document.write( "in 20 years, he needs to have enough invested so that he can withdraw 10,000 every month for 10 years at 8% compounded monthly.\r<BR>\n" );
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document.write( "the present value of that annuity at 8% compounded monthly with 10,000 dollars taken out at the end of every month is equal to 824,214.81.\r<BR>\n" );
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document.write( "that amount is how much he needs at the end of 20 years.\r<BR>\n" );
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document.write( "today, he invests 50,000 at 10% per quarter for 20 years and he also invests a certain amount of money at the end of every half year for 20 years, the sum of which must be equal to 824,214.81 in 20 years.\r<BR>\n" );
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document.write( "the 50,000 invested today at 10% compounded quarterly is worth 360,478.39 in 20 years.\r<BR>\n" );
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document.write( "he needs 824,214.81.<BR>\n" );
document.write( "the difference of what he needs minus what he earns on the 50,000 investment is equal to 824,214.81 minus 360,,478.39 = 463,736.42.\r<BR>\n" );
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document.write( "the amount of money he needs to invest every 6 months to equal that money at 7% per year compounded semi-annually is equal to 5484.74.\r<BR>\n" );
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document.write( "between the 50,000 he invests today and the 5484.74 that he invests every 6 months, he will have 824,214.81 invested in 20 years with which he can draw 10,000 at the end of every month for the next 10 years.\r<BR>\n" );
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document.write( "here's an online calculator that provides you with these results.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://arachnoid.com/finance/index.html\" target = \"_blank\">https://arachnoid.com/finance/index.html</a>\r<BR>\n" );
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document.write( "the first display is the result of finding the present value of 120 payments of 10,000 at the end of each month at 8% per year compounded monthly.\r<BR>\n" );
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document.write( "inputs were:<BR>\n" );
document.write( "fv = 0<BR>\n" );
document.write( "np = 10 years * 12 months per year = 120<BR>\n" );
document.write( "pmt = 10,000<BR>\n" );
document.write( "ir = 8% per year / 12 months per year = .6666666..... rounded to the display size.<BR>\n" );
document.write( "payments made at end of each month.<BR>\n" );
document.write( "output was:<BR>\n" );
document.write( "pv = -824,214.81\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/110404.jpg\" >\r<BR>\n" );
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document.write( "the second display is the result of finding the future value of 50,000 invested at 10% compounded quarterly for 20 years.\r<BR>\n" );
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document.write( "inputs were:<BR>\n" );
document.write( "pv= -50,000<BR>\n" );
document.write( "np = 20 years * 4 quarters per year = 80<BR>\n" );
document.write( "pmt = 0<BR>\n" );
document.write( "ir = 10% per year divided by 4 quarters pe year = 2.5<BR>\n" );
document.write( "output was:<BR>\n" );
document.write( "fv = 360,478.39\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/110402.jpg\" >\r<BR>\n" );
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document.write( "the third display is the result of finding the payments required at the end of each semi-annual period at invested 7% compounded semi-annually for 20 years that you want to be equal to  824,214.81 minus 360,478.39 = 463,736.42 in 20 years.\r<BR>\n" );
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document.write( "inputs were:<BR>\n" );
document.write( "pv = 0<BR>\n" );
document.write( "fv = 463,736.42<BR>\n" );
document.write( "np = 20 years * 2 semi-annual periods per year = 40<BR>\n" );
document.write( "ir = 7% per year / 2 semi-annual periods per year = 3.5<BR>\n" );
document.write( "payments made at the end of each semi-annual period.<BR>\n" );
document.write( "output was:<BR>\n" );
document.write( "pmt = -5484.74\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/110403.jpg\" >\r<BR>\n" );
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document.write( "money coming in to you was shown as positive.<BR>\n" );
document.write( "money going out from you was shown as negative.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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