document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=838191>Question 838191</A>: <I><SPAN STYLE=\"word-break: break-all;\"> City Wide Delivery Service uses vans costing $24800 each. How much will the company have to invest today to accumulate enough money to buy six new vans at the end of 4 years? City Wide's bank is currently paying 12% interest compounded quarterly.<BR>\n" );
document.write( "a)92727<BR>\n" );
document.write( "b)24500<BR>\n" );
document.write( "c)15000<BR>\n" );
document.write( "d) 14525 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #504897 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=504897\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> each van costs 24,800<BR>\n" );
document.write( "6 new vans will cost 24,800 * 6 = 148,800.\r<BR>\n" );
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document.write( "the number of years is 4.<BR>\n" );
document.write( "the number of compounding periods per year is 4 (quarterly).<BR>\n" );
document.write( "the number of time periods involved is therefore 4 * 4 = 16 quarterly time periods.\r<BR>\n" );
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document.write( "the annual interest rate is 12%.<BR>\n" );
document.write( "if you pay interest rate quarterly, then the quarterly interest rate is 12% / 4 = 3% per quarter.\r<BR>\n" );
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document.write( "the decimal equivalent of 3% is .03\r<BR>\n" );
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document.write( "the formula you will use is:\r<BR>\n" );
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document.write( "f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "f is equal to the amount of money you will be paying for the vans in 4 years.<BR>\n" );
document.write( "p is the amount of money you will need to today in order to do that.<BR>\n" );
document.write( "r is equal to the quarterly compounding rate which is equal to .03.<BR>\n" );
document.write( "n is equal to the number of quarterly compounding periods which is equal to 16.\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "148,800 = p * (1 + .03) ^ 16\r<BR>\n" );
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document.write( "this can be written as:\r<BR>\n" );
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document.write( "148800 = p * (1.03)^16\r<BR>\n" );
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document.write( "divide both sides of this equation by (1.03)^16 and you get:\r<BR>\n" );
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document.write( "148800 / (1.03)^16 = p\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "148800 / 1.604706439 = p\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "p = 92727.24056\r<BR>\n" );
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document.write( "this can be written as:\r<BR>\n" );
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document.write( "p = $92,727.25 rounded to the next highest penny.\r<BR>\n" );
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document.write( "you will need to invest $92,727.25 today in order to have at least $148,800 in 4 years.\r<BR>\n" );
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document.write( "$92,727.25 invested at 3% per quarter for 16 quarters comes out to be:\r<BR>\n" );
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document.write( "92727.25 * (1.03)^16 which is equal to 148800.0152  which can be written as:\r<BR>\n" );
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document.write( "$148,800.02 rounded to the nearest penny.\r<BR>\n" );
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document.write( "your answer would be selection a which is 92727.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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