document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143251>Question 1143251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bobby would like to take a trip to Greece in 5 years.  He will need $1,575 monthly while he is there and expects to remain there for 8 months.  If money is worth 3.9% compounded monthly, how much will Bobby need to deposit now in order to make his trip to Greece become a reality?  Assume he will need the money at the BEGINNING of each month.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #764076 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=764076\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> he will need 1575 at the beginning of each month for 8 months.<BR>\n" );
document.write( "the money is worth 3.9% compounded monthly.\r<BR>\n" );
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document.write( "there are two pieces to this problem.<BR>\n" );
document.write( "first is to find the present value of the annuity for 8 months.<BR>\n" );
document.write( "second is to find the present value of that amount for 5 years.\r<BR>\n" );
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document.write( "both these amounts can be found by formula or by calculator.<BR>\n" );
document.write( "i'll do calculator.<BR>\n" );
document.write( "if you need formula, then come back to me and i will give you bormula.\r<BR>\n" );
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document.write( "the clculator i used is the TI-BA-II business analyst calculator.\r<BR>\n" );
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document.write( "my inputs to this calculator for the annuity are:\r<BR>\n" );
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document.write( "present value = 0<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "payment at the beginning of each is 1575 for 8 months.<BR>\n" );
document.write( "interest rate percent per month is 3.9/12 = .325.\r<BR>\n" );
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document.write( "calculator tells me that the present value for the annuity is equal to 12,458.06115\r<BR>\n" );
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document.write( "that's the amount of money needed in 5 years.\r<BR>\n" );
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document.write( "that's the future value of an amount of money for 5 years at 3.9% per year compounded monthly.\r<BR>\n" );
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document.write( "i then tell the calculator the following.\r<BR>\n" );
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document.write( "present value = 0<BR>\n" );
document.write( "future value = 12,458.06115<BR>\n" );
document.write( "monthly payment = 0<BR>\n" );
document.write( "interest rate percent per month = 3.9 / 12 = .325.<BR>\n" );
document.write( "time period is 5 years * 12 = 60 months.\r<BR>\n" );
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document.write( "calculator tells me that the present value is equal to 10,254.16624.\r<BR>\n" );
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document.write( "i repeated the procedure with an online financial calculator that tells me the following.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/071901.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/071902.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "i basically used the same procedure as i did with the TI-BA-II calculator.\r<BR>\n" );
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document.write( "this calculator can be found online at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "the calculators require that, if the payment is negative, than the present value or future value will be positive.\r<BR>\n" );
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document.write( "they also require that, if the present value is negative, the future value will be positive, and vice versa.\r<BR>\n" );
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document.write( "where you have to remember this is when you input both present value and payment, or present value and future value.<BR>\n" );
document.write( "one of them has to be negative and the other has to be positive or the calculator will not be able to give you a result.\r<BR>\n" );
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document.write( "the cash flow rule is that money going out is negative and money coming in is positive.\r<BR>\n" );
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document.write( "for example, you wanted 1575 to come in to you each month, so that is positive.<BR>\n" );
document.write( "the investment required to get that (the present value) is therefore shown as negative because that's money you have to shell out at the beginning of the 8 month period.\r<BR>\n" );
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document.write( "the difference between what the TI-BA-II calculates and what the online calculator calculates is due to rounding.<BR>\n" );
document.write( "the TI doesn't round intermediate results.<BR>\n" );
document.write( "the online calculator does (rounds to the nearest penny as far as i can tell).<BR>\n" );
document.write( "the difference is usually minimal, as can be seen in the results shown for both.\r<BR>\n" );
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document.write( "any questions, contact dtheophilis@gmail.com\r<BR>\n" );
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