document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133089>Question 1133089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of workers won the lottery and will each walk away with $10 000. Fred, one of the workers,  decides to spend some of the money and save the rest. He wants the money he saves to grow back into $10 000 in 7 years. He can invest the money at 5.5% compounded quarterly.\r<BR>\n" );
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document.write( "a) How much must he invest to meet his goal.\r<BR>\n" );
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document.write( "b) How much money can he afford to spend today?\r<BR>\n" );
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document.write( "(I have been working on this problem and i did get for R=4657.65 and i am not sure what they mean by part b.)<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 #750266 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=750266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">Part (a)\r<BR>\n" );
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document.write( "We'll use the compound interest formula shown below\r<BR>\n" );
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document.write( "A = P*(1+r/n)^(n*t)\r<BR>\n" );
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document.write( "The variables are<BR>\n" );
document.write( "A = final amount<BR>\n" );
document.write( "P = initial amount (aka deposit)<BR>\n" );
document.write( "r = annual interest rate in decimal form<BR>\n" );
document.write( "n = number of times money is compounded per year<BR>\n" );
document.write( "t = number of years\r<BR>\n" );
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document.write( "In this case, we have,<BR>\n" );
document.write( "A = 10000 is the final amount we want to have<BR>\n" );
document.write( "P = unknown initial amount or deposit (what we want to solve for)<BR>\n" );
document.write( "r = 0.055 is the decimal form of 5.5% (note how 5.5% = 5.5/100 = 0.055)<BR>\n" );
document.write( "n = 4 means we compound 4 times a year, in other words, quarterly<BR>\n" );
document.write( "t = 7 years pass by\r<BR>\n" );
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document.write( "Let's plug those mentioned values into the formula. Solve for P.\r<BR>\n" );
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document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "10000 = P*(1+0.055/4)^(4*7)<BR>\n" );
document.write( "10000 = P*(1+0.01375)^(28)<BR>\n" );
document.write( "10000 = P*(1.01375)^(28)<BR>\n" );
document.write( "10000 = P*1.46576478021002<BR>\n" );
document.write( "1.46576478021002*P = 10000<BR>\n" );
document.write( "P = 10000/1.46576478021002<BR>\n" );
document.write( "P = 6,822.37705190812<BR>\n" );
document.write( "P = 6,822.38\r<BR>\n" );
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document.write( "--------------------\r<BR>\n" );
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document.write( "Answer: <font color=red>6822.38 dollars</font>\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "Whatever we found back in part (a) represents the amount needed to be put aside to save back to $10,000. The rest can be spent. <BR>\n" );
document.write( "Subtract the result found in part (a) from 10,000 to get: 10,000 - 6,822.38 = 3,177.62\r<BR>\n" );
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document.write( "--------------------\r<BR>\n" );
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document.write( "Answer: <font color=red>3177.62 dollars</font>\r<BR>\n" );
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