document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698913>Question 698913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. I kind of understand how a total salary amount over a certain period of years with a fixed annual increase using arithmetic series is done but how does one do this if the annual rate of increase is a percentage?  e.g. What would be the total amount of a salary that starts at $20,000 per year at an annual increase of 5% over 10 years? Thank you. Paul Stone </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #431151 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10555)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=431151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Hi. I kind of understand how a total salary amount over a certain period of years with a fixed annual increase using arithmetic series is done but how does one do this if the annual rate of increase is a percentage?  e.g. What would be the total amount of a salary that starts at $20,000 per year at an annual increase of 5% over 10 years? Thank you. Paul Stone\r<BR>\n" );
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document.write( "This is the equivalent of asking one to determine the future value, after 10 years, of $20,000, which is compounded annually, at a rate of 5%.\r<BR>\n" );
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document.write( "The future value formula, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+P%281+%2B+r%2Fm%29%5E%28tm%29 ALIGN=MIDDLE  ALT=\"A+=+P%281+%2B+r%2Fm%29%5E%28tm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be used, with A being the future value, or value after 10 years, P = present value, or $20,000, r = rate of interest, or 5% (.05), m being the amount of compounding periods per year, and t being the time, in years (10)\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+P%281+%2B+r%2Fm%29%5E%28tm%29 ALIGN=MIDDLE  ALT=\"A+=+P%281+%2B+r%2Fm%29%5E%28tm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281+%2B+.05%2F1%29%5E%2810+%2A+1%29 ALIGN=MIDDLE  ALT=\"A+=+20000%281+%2B+.05%2F1%29%5E%2810+%2A+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+20000%281.05%29%5E10 ALIGN=MIDDLE  ALT=\"A+=+20000%281.05%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A, or amount in 10 years = 20000(1.628894627), or $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2832577.89%29 ALIGN=MIDDLE  ALT=\"highlight_green%2832577.89%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can do the check!!\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at MathMadEzy@aol.com </SPAN>\n" );
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