document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130840>Question 1130840</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At the age 18 you start to work for a company and are offered two rather fanciful retirement options. <BR>\n" );
document.write( "Retirement 1 option: When you retire, you will be paid a lump sum of $15,000 for each year of service<BR>\n" );
document.write( "Retirement 2 option: When you start to work, the company will deposit $10,000 into an account that pays 9.6% interest compounded monthly. When you retire, the account will be closed and the balance is given to you.<BR>\n" );
document.write( "(a) Which retirement option is more favorable if you retire at age 65\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747469 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=747469\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(I will assume this post is from the same person who submitted the same question for a worker who retires at 55...)<br><BR>\n" );
document.write( "Option 1: $15000 a year for 47 years: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=47%2A15000+=+705000 ALIGN=MIDDLE  ALT=\"47%2A15000+=+705000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Option 2: $10000, multiplied by 1.008 (1 plus the monthly interest rate) for (12*47) months: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%281.008%5E%2812%2A47%29%29+=+894829.12 ALIGN=MIDDLE  ALT=\"10000%281.008%5E%2812%2A47%29%29+=+894829.12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For working 47 years, the single deposit earning compound interest is substantially higher.<br><BR>\n" );
document.write( "Comparing the two problems with the different numbers of years of service, you can see that the amount from Option 1 is a linear relationship with the number of years, whereas the amount from Option 2 grows exponentially.  Because of the smaller initial investment amount, Option 1 is still better for 37 years of service; the exponential growth of Option 2 hasn't quite caught up with the linear growth from Option 1.  But by 47 years of service the amount from Option 2 with is exponential growth has far surpassed the linear growth of Option 1.<br><BR>\n" );
document.write( "-------------------------------------------------<BR>\n" );
document.write( "comment from student:<br><BR>\n" );
document.write( "Now I'm confused with your numbers. So option 1 would be 15,000 for 65 years instead of 47? How did you get 1.008?<br><BR>\n" );
document.write( "(1) Option 1 is $15000 for each year the employee worked for the company.  Starting at age 18 and working until age 65 is 47 years.<BR>\n" );
document.write( "(2) The annual percentage rate for Option 2 is 9.6% = 0.096.  The monthly interest rate is 1/12 of that: 0.008.  The monthly GROWTH FACTOR is 1+.008 = 1.008. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );