document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208034>Question 208034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you are offered two jobs. One pays $30,000 the first year with annual raises of $2000 each year. The second offers a starting salary of $27,000 and raises of 8% each year. At the end of ten years, what would your yearly salary be from a) the first job? b)the second job?<BR>\n" );
document.write( "My answer; $30,000=1 year + $2000=each coming year * 10 years<BR>\n" );
document.write( "but since the first year is already given I dont have to count it with do I? (thats why I am not sure if I got this right)<BR>\n" );
document.write( "a) 2000*9=18,000 30,000+18,000=48,000 so $48,000 after 10 years<BR>\n" );
document.write( "b)27,000=1 year + 8% each coming year * 10 years<BR>\n" );
document.write( "(here again I only put 9 years to count, since 27,000 already is the first year, or is that wrong?)<BR>\n" );
document.write( "270*8=2,160  2,160*9=19,440 27,000+19,440=46,440 so $46,440 after 10 years<BR>\n" );
document.write( "Could someone please tell me if I solved the problem right?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157344 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=157344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose you are offered two jobs. One pays $30,000 the first year with annual raises of $2000 each year. The second offers a starting salary of $27,000 and raises of 8% each year. At the end of ten years, what would your yearly salary be from a) the first job? b)the second job?<BR>\n" );
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document.write( "If we assume that the salary increase is at the end of each year, we get the following:<BR>\n" );
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document.write( "first job would be $30,000 + (10 * $2,000) = $50,000<BR>\n" );
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document.write( "second job would be $27,000 * (1.08)^10 = $58,290.97<BR>\n" );
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document.write( "If we assume that the salary increase is at the beginning of each year, we get the following:<BR>\n" );
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document.write( "first job would be $30,000 + (9 * $2,000) = $48,000<BR>\n" );
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document.write( "second job would be $27,000 * (1.08)^9 = $53,973.12<BR>\n" );
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document.write( "It doesn't really matter whether you used 9 years or 10 years<BR>\n" );
document.write( "because you will be making more money at the second job either way.<BR>\n" );
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document.write( "They are asking:<BR>\n" );
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document.write( "At the end of ten years, what would your yearly salary be from a) the first job? b)the second job?<BR>\n" );
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document.write( "This is nebulous and clearly open to interpretation.  They do not clearly state when you get the annual salary increase.<BR>\n" );
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document.write( "In a real world situation you would have had to ask for a clarification as to they wanted you to make the calculations.<BR>\n" );
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document.write( "your answer should include:<BR>\n" );
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document.write( "if they get a raise at the end of each year, then at the end of the 10th year the annual salary would be.<BR>\n" );
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document.write( "your alternate answer should include:<BR>\n" );
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document.write( "if they get a raise at the beginning of the next year, then at the end of the 10th year, the annual salary would be.<BR>\n" );
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document.write( "in the first case, carrying out the operations 10 years would be correct.<BR>\n" );
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document.write( "in the alternate case, carrying out the operations 9 years would be correct.<BR>\n" );
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document.write( "when you do the 8% solution, you are doing compound interest, not simple interest.<BR>\n" );
document.write( "simple interest would be $27,000 + (.08*10*27000)<BR>\n" );
document.write( "compound interest would be $27,000 * (1.08)^10 as shown.<BR>\n" );
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document.write( "first proposal yearly salary with raises at the end of each year would look like this.<BR>\n" );
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document.write( "end of year 1: $32,000<BR>\n" );
document.write( "end of year 2: $34,000<BR>\n" );
document.write( "end of year 3: $36,000<BR>\n" );
document.write( "end of year 4: $38,000<BR>\n" );
document.write( "end of year 5: $40,000<BR>\n" );
document.write( "end of year 6: $42,000<BR>\n" );
document.write( "end of year 7: $44,000<BR>\n" );
document.write( "end of year 8: $46,000<BR>\n" );
document.write( "end of year 9: $48,000<BR>\n" );
document.write( "end of year 10: $50,000<BR>\n" );
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document.write( "first proposal yearly salary with raises at the end of each year would look like this.<BR>\n" );
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document.write( "end of year 1: $30,000<BR>\n" );
document.write( "end of year 2: $32,000<BR>\n" );
document.write( "end of year 3: $34,000<BR>\n" );
document.write( "end of year 4: $36,000<BR>\n" );
document.write( "end of year 5: $38,000<BR>\n" );
document.write( "end of year 6: $40,000<BR>\n" );
document.write( "end of year 7: $42,000<BR>\n" );
document.write( "end of year 8: $44,000<BR>\n" );
document.write( "end of year 9: $46,000<BR>\n" );
document.write( "end of year 10: $48,000<BR>\n" );
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document.write( "he doesn't get $50,000 until the beginning of the 11th year.<BR>\n" );
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document.write( "same concept applies for the 8% case.<BR>\n" );
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document.write( "Without knowing, you need to qualify your answer as I indicated and I would think you need to show both answers with the qualification for each.<BR>\n" );
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document.write( "My answer would be:<BR>\n" );
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document.write( "If the salary increases at the end of each year, then:<BR>\n" );
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document.write( "first job would be paying $30,000 + (10 * $2,000) = $50,000 and the second job would be $27,000 * (1.08)^10 = $58,290.97<BR>\n" );
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document.write( "If the salary increases at the beginning of each year, then:<BR>\n" );
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document.write( "first job would be paying $30,000 + (9 * $2,000) = $48,000 and the second job would be $27,000 * (1.08)^9 = $53,973.12<BR>\n" );
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