document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028986>Question 1028986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have some question on how to understand this type of problems. I would like to know what could be the best way to understand it. \r<BR>\n" );
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document.write( "A) Suppose you enroll in an IRA that pays an APR of 8%, compounded monthly, if you contribute $90/month for 15 years how will the IRA contain at the end of that time? \r<BR>\n" );
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document.write( "B) Suppose you contribute $110 how much will the IRA contain?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644049 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=644049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the easiest way to figure this out is to use a financial calculator.<BR>\n" );
document.write( "one such calculator can be found here.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://arachnoid.com/finance/index.html\" target = \"_blank\">http://arachnoid.com/finance/index.html</a>\r<BR>\n" );
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document.write( "using this calculator, you would divide the annual percentage rate by 12 to get the monthly percentage rate.\r<BR>\n" );
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document.write( "you would multiply the number of years by 12 to get the number of months.\r<BR>\n" );
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document.write( "you would enter the monthly payment as a negative number (it's what you are paying out, so it's negative).\r<BR>\n" );
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document.write( "you would leave the present value and future value as 0.\r<BR>\n" );
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document.write( "you would set the payments to be at the end of the period (this is usually what is done).\r<BR>\n" );
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document.write( "you would then click on the FV button and it will tell you how much money you would have at the end of the 15 year period.\r<BR>\n" );
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document.write( "the assumption is that all interest earned in the intermediate years is re-invested immediately into the annuity fund.\r<BR>\n" );
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document.write( "your results will be as shown below:\r<BR>\n" );
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document.write( "the first one shows 90 invested monthly.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/041001.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the second one shows 110 invested monthly.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/041002.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the link to the calculator also shows the formulas used.  \r<BR>\n" );
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document.write( "they can be a bit hard to follow, but they'll give you the same answer if you give them the right information.\r<BR>\n" );
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document.write( "the formulas work from the interest rate and not the interest percentage rate.\r<BR>\n" );
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document.write( "basically you take the percentage rate and divide it by 100 to get the rate.\r<BR>\n" );
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document.write( "the key is in the time intervals involved.\r<BR>\n" );
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document.write( "with monthly compounding, the annual rate is divided by 12 and the number of years if multiplied by 12.\r<BR>\n" );
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document.write( "the actual month by month calculations are shown in the following spreadsheet.\r<BR>\n" );
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document.write( "only the first several months are shown, and then only the last several months are shown.\r<BR>\n" );
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document.write( "the stuff in the middle is just more of the same.\r<BR>\n" );
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document.write( "multiplying the previous month's remaining balance by (1 + .08/12) gives you the previous month's remaining balance plus the interest that is earned by it.<BR>\n" );
document.write( "you then add the monthly payment to that to get the current month's remaining balance.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/041003.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/041004.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you can see that the spreadsheet analysis and the financial formulas give you the same result.\r<BR>\n" );
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