document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073431>Question 1073431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is present value of annuity of 2300 payable at the end of each 8 months for 5 years if money is worth 4% compounded semiannually </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688265 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=688265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the present value will be equal to 14506.5338\r<BR>\n" );
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document.write( "your nominal annual interest rate is .04\r<BR>\n" );
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document.write( "divide that by 2 and you get a semi-annual interest rate of .02\r<BR>\n" );
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document.write( "your time periods are in semi-annual increments.\r<BR>\n" );
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document.write( "your semi-annual interest rate can be converted into an equivalent monthly rate by use of the following formula.\r<BR>\n" );
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document.write( "monthly interest rate = (1 + .01) ^ (1/6) - 1 = .00330589\r<BR>\n" );
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document.write( "the payments are made at the end of:\r<BR>\n" );
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document.write( "month 8<BR>\n" );
document.write( "month 16<BR>\n" );
document.write( "month 24<BR>\n" );
document.write( "month 32<BR>\n" );
document.write( "month 40<BR>\n" );
document.write( "month 48<BR>\n" );
document.write( "month 56\r<BR>\n" );
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document.write( "the present value for each of these periods would be:\r<BR>\n" );
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document.write( "2300 / 1.00330589 ^ 8 = 2240.066<BR>\n" );
document.write( "2300 / 1.00330589 ^ 16 = 2181.695<BR>\n" );
document.write( "2300 / 1.00330589 ^ 24 = 2124.844<BR>\n" );
document.write( "2300 / 1.00330589 ^ 32 = 2069.475<BR>\n" );
document.write( "2300 / 1.00330589 ^ 40 = 2015.549<BR>\n" );
document.write( "2300 / 1.00330589 ^ 48 = 1963.028<BR>\n" );
document.write( "2300 / 1.00330589 ^ 56 = 1911.875\r<BR>\n" );
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document.write( "add these present values up and you get 14506.53 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "you should be able to use the present worth of annuity formulas also, if you translate the semi-annual interest rate into an 8 month equivalent interest rate.\r<BR>\n" );
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document.write( "that should be equal to 1.02 ^ (8/6) = 1.026755164 - 1 = .026755164\r<BR>\n" );
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document.write( "this is the equivalent 8 month effective interest rate taken from the semi-annual interest rate of 2%.\r<BR>\n" );
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document.write( "since you have 7 payments, then your present value should be equivalent to an annuity where the 8 month interest rate is .026755164 and you are taking the present value of 2300 for seven 8 month periods.\r<BR>\n" );
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document.write( "keep in mind that an interest rate of.026755164 is equal to 2.6755164%.\r<BR>\n" );
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document.write( "i used an online time value of money calculator to demonstrate that you will get the same present value.\r<BR>\n" );
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document.write( "using this calculator, your inputs would be as shown in the following picture.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/031901.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "once you click on pv, then your present value will be as shown in the following picture.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/031902.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you can see that the equivalent interest rates are accurate when you look at time periods that are coincident.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "8 semi-annual periods are the same as 6 eight month periods.\r<BR>\n" );
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document.write( "they are both equivalent to 48 months.\r<BR>\n" );
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document.write( "so, if you have 1000 at the end of 8 semi-annual periods, then the present value will be 1000 / 1.02 ^ 8 = 853.4903712, and if you have 1000 at the end of 6 eight month periods, then the present value will be 1000 / 1.026755164 ^ 6 = 853.4903699, and if you have 1000 at the end of 48 one month periods, then the present value will be 1000 / 1.00330589 ^ 48 = 853.4903844.\r<BR>\n" );
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document.write( "it's the same present value.\r<BR>\n" );
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document.write( "what is not considered is what happens after the 56th month.\r<BR>\n" );
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document.write( "the 5 year period is 60 months.\r<BR>\n" );
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document.write( "the assumption is that your last payment is in the 56th month and you get no more payments.\r<BR>\n" );
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document.write( "no credit is given for any payments after that, partial or otherwise.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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