document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177372>Question 1177372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company loaned 300 of its machines to a subsidiary company. If the subsidiary company was able to generate 7% compounded each quarter on its invested money, what total amount does it need to invest to purchase these machines within 18 months at a price of $300,000 each? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #806332 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=806332\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the total cost of the machines is 300 * 300,000 = 3 * 10^2 * 3 * 10^5 = 9 * 10^7 = 90,000,000 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the subsidiary company is able to generate 7% per year compounded quarterly on its invested money.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it needs to have 90 million dollars within 18 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1 quarter is equal to 3 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "18 months / 3 = 6 quarters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula to use is f = p * (1 + r) ^ n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the time periods are in quarters, you need to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide 7% per year by 4 to get (7/4)% per quarter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the formula works on rate rather than percent, you need to divide that by 100 to get a rate of 7/400 per quarter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the number of quarters is 18 / 3 = 6 quarters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's because 1 quarter is equal to 3 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the future value is 90 million.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's how much is needed in 18 months to buy the machines.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "90 million = p * (1 + 7/400) ^ 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by (1 + 7/400) ^ 6 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "90 million / (1 + 7/400) ^ 6 = p\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for p to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p = 81.10281875 million.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "confirm by replacing p in the original equation with that and solve for f to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 81.10282875 * (1 + 7/400) ^ 6 = 90 million.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your solution is that the subsidiary company needs to invest 81.10282875 million now so that it can have 90 million available to purchase the machines in 18 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );