document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=705339>Question 705339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Example: (Present Value)\r<BR>\n" );
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document.write( "Tony is investing $5000 at 6% per annum, compounded quarterly for 3 years. Then, he will invest that amount along with some additional money at 7.25% per anum, compounded monthly for 3 more years so as to have $12500 at the end of six years. How much additional money must he invest?\r<BR>\n" );
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document.write( "(I tried using the formula A = P(1+i)^n which is the compound interest formula, but since present value is included, I don't know what to do. The formula that was included is PV = A/(1 + i)^n)\r<BR>\n" );
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document.write( "I will appreciate it if you're able to help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434521 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=434521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Start with 5000 for 3 years at 6% per annnum compounded quarterly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5000(1.015)^{12}\ \approx\ $5978.09\">\r<BR>\n" );
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document.write( "Now, if you invested ONLY that amount for an additional 3 years at 7.5% per annum compounded monthly, you would have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5978.09(1.00625)^{36}\ \approx\ $7481.26\">\r<BR>\n" );
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document.write( "Which is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 12500\ -\ 7481.26\ =\ 5018.24\"> short of your goal.\r<BR>\n" );
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document.write( "So the question becomes what do I need to invest for 3 years at 7.5% per annum compounded monthly to achieve $5018.24?  In other words, what is the PV of A = $5018.24, 3 years, 7.5%, monthly:\r<BR>\n" );
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document.write( "For this you need:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ PV\ =\ \frac{$5018.24}{(1.00625)^{36}}\">\r<BR>\n" );
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document.write( "I'll leave that last little bit of arithmetic to you.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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