document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204380>Question 1204380</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A newscaster earns $26,100 and wants to invest 10% of his/her monthly salary to save for retirement in 38 years. If he/she invests this money at 5.1% compounded monthly, how much money will he/she have at retirement?\r<BR>\n" );
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document.write( "How much will be saved each year?<BR>\n" );
document.write( "What will be the amount in the account after 38 years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840593 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840593\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "A newscaster earns $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26100 ALIGN=MIDDLE  ALT=\"26100\"   DISABLED_style= \"max-width:90%; height:auto;\" > => assuming this is annual salary<BR>\n" );
document.write( "wants to invest <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >% of his/her <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=monthly ALIGN=MIDDLE  ALT=\"monthly\"   DISABLED_style= \"max-width:90%; height:auto;\" > salary to save for retirement in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38 ALIGN=MIDDLE  ALT=\"38\"   DISABLED_style= \"max-width:90%; height:auto;\" > years\r<BR>\n" );
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document.write( "If he/she invests this money at<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5.1 ALIGN=MIDDLE  ALT=\"+5.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >% compounded monthly, how much money will he/she have at retirement?\r<BR>\n" );
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document.write( "a) How much will be saved each year?\r<BR>\n" );
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document.write( "we first need to calculate  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >% =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1 ALIGN=MIDDLE  ALT=\"0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" > of $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26100 ALIGN=MIDDLE  ALT=\"26100\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "Annual savings = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26100+%2A+0.1 ALIGN=MIDDLE  ALT=\"26100+%2A+0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Annual savings = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2610 ALIGN=MIDDLE  ALT=\"2610\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, the newscaster will save $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2610 ALIGN=MIDDLE  ALT=\"2610\"   DISABLED_style= \"max-width:90%; height:auto;\" > each year.\r<BR>\n" );
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document.write( "What will be the amount in the account after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38+ ALIGN=MIDDLE  ALT=\"38+\"   DISABLED_style= \"max-width:90%; height:auto;\" >years?\r<BR>\n" );
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document.write( "To find the amount in the account after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38+ ALIGN=MIDDLE  ALT=\"38+\"   DISABLED_style= \"max-width:90%; height:auto;\" >years, we will use the formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+P+%2A%28%281+%2B+r%29%5E%28nt%29+-+1%29+%2F+r ALIGN=MIDDLE  ALT=\"FV+=+P+%2A%28%281+%2B+r%29%5E%28nt%29+-+1%29+%2F+r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+ ALIGN=MIDDLE  ALT=\"FV+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the future value, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+ ALIGN=MIDDLE  ALT=\"P+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=monthly ALIGN=MIDDLE  ALT=\"monthly\"   DISABLED_style= \"max-width:90%; height:auto;\" > deposit,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+ ALIGN=MIDDLE  ALT=\"+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the monthly interest rate (annual interest rate divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of times interest is compounded per year (monthly, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of years.\r<BR>\n" );
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document.write( " find the monthly deposit, we need to divide the annual savings by the number of months in a year:\r<BR>\n" );
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document.write( "Monthly deposit =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2610+%2F+12 ALIGN=MIDDLE  ALT=\"+2610+%2F+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Monthly deposit <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+217.5 ALIGN=MIDDLE  ALT=\"P+=+217.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, we have:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+217.5 ALIGN=MIDDLE  ALT=\"P+=+217.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "convert <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.1 ALIGN=MIDDLE  ALT=\"5.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >% to decimal:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.051 ALIGN=MIDDLE  ALT=\"0.051\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+0.051%2F12=0.00425 ALIGN=MIDDLE  ALT=\"r+=+0.051%2F12=0.00425\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+12 ALIGN=MIDDLE  ALT=\"n+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > months\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+38 ALIGN=MIDDLE  ALT=\"t+=+38\"   DISABLED_style= \"max-width:90%; height:auto;\" > years\r<BR>\n" );
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document.write( "Now, plug the values into the formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+217.5+%2A%28%281+%2B+0.00425%29%5E%2812%2A38%29+-+1%29+%2F%280.00425%29 ALIGN=MIDDLE  ALT=\"FV+=+217.5+%2A%28%281+%2B+0.00425%29%5E%2812%2A38%29+-+1%29+%2F%280.00425%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=302779.76 ALIGN=MIDDLE  ALT=\"FV+=302779.76\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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