document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162034>Question 1162034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Frank received a 380,000 dollar inheritance on his 30th birthday and invested it into a fund that earns 5.3%, compounded semiannually. If this amount is deferred until Frank’s 60th birthday, how much will it provide at the end of each half-year for the next 10 years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785842 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=785842\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> frank received 380,000 dollars on his 30th birthday.<BR>\n" );
document.write( "he invest it at 5.3% compounded semi-annually until his 60th birthday.<BR>\n" );
document.write( "how much will it provide at the end of each half year for the next 10 years (until his 70th birthday).\r<BR>\n" );
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document.write( "first you need to get the future value of 300,000 for 30 years.<BR>\n" );
document.write( "formula is f = p * (1 + r) ^ n<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "formula becomes:<BR>\n" );
document.write( "f = 380,000 * (1 + .053/2) ^ (30 * 2) = 1,825,243.5326.<BR>\n" );
document.write( ".053/2 is the interest rate per half year.<BR>\n" );
document.write( "30 * 2 is the number of half years.<BR>\n" );
document.write( "380,000 is the present value.\r<BR>\n" );
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document.write( "at the end of the 30 year period, he has 1,825,24.536 to draw from at the end of each half year for the next 10 years.\r<BR>\n" );
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document.write( "the formula to use is the annuity from a present value formula with end of time period payments.\r<BR>\n" );
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document.write( "that formula is shown below:\r<BR>\n" );
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document.write( "ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS\r<BR>\n" );
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document.write( "a = (p*r)/(1-(1/(1+r)^n))\r<BR>\n" );
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document.write( "a is the annuity.<BR>\n" );
document.write( "p is the present amount.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "that formula becomes:\r<BR>\n" );
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document.write( "a = (1825243.536*.053/2)/(1-(1/(1+.053/2)^(10*2))) = 118,749.5326.\r<BR>\n" );
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document.write( "the future value from the first formula becomes the present value in the second formula.<BR>\n" );
document.write( "the interest rate is still .053/2.<BR>\n" );
document.write( "the number of time periods becomes 10*2.\r<BR>\n" );
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document.write( "he will be able to draw 118,749.5326 at the end of each half year period for the next 10 years until he's 70.\r<BR>\n" );
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document.write( "you could have solved this using a financial calculator as well.<BR>\n" );
document.write( "here are the results from using the financial calculator online at <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( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/070801.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/070802.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "this calculator requires percent, not rate.<BR>\n" );
document.write( "if the present value is entered as negative, the future value comes out at positive.<BR>\n" );
document.write( "the time periods have to be specific, i.e. 60 rather than 30/2 or 20 rather than 20/2.<BR>\n" );
document.write( "the interest rate has to be specific, i.e. 2.65 rather than 5.3/2.<BR>\n" );
document.write( "the first use of the calculator finds the future value.<BR>\n" );
document.write( "that future value becomes the present value in the second use of the calculator.<BR>\n" );
document.write( "10 years * 2 is entered as 20 in the second use of the calculator.<BR>\n" );
document.write( "the present value is entered as negative and the payment per time period comes out positive.\r<BR>\n" );
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document.write( "you get the same answer whether you use the calculator or the formula, as you should.<BR>\n" );
document.write( "this calculator, however, rounds your answers to the nearest penny.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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