document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097941>Question 1097941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following has a lower present value?\r<BR>\n" );
document.write( "\n" );
document.write( "$90,000 if interest is paid at a rate of 5.44% compounded continuously for 2 years\r<BR>\n" );
document.write( "\n" );
document.write( "$96,000 if interest is paid at a rate of 3.4% compounded continuously for 29 months </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712454 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=712454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> continuous compounding formula is f = p * e^(r*n)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r id the interest rate per time period<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for p to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p = f / e^(r*n)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the one thing that you have to do is to keep the time periods consistent.<BR>\n" );
document.write( "if your interest rate is in time periods and your number of time periods are different, you will not get the right answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "first problem gets you:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 90,000<BR>\n" );
document.write( "p = what you want to find.<BR>\n" );
document.write( "r = .0544 per year<BR>\n" );
document.write( "n = 2 years.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "time periods are the same so just solve.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p = f / e^(r*n) becomes p = 90,000 / e^(.0544*2).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this gets you p = 80721.88034\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "second problem gets you:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 96,000<BR>\n" );
document.write( "p = what you want to find.<BR>\n" );
document.write( "r = .034 per year<BR>\n" );
document.write( "n = 29 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you either have to convert interest rate per year to months or you have to convert months to years.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "converting months to years, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 96,000<BR>\n" );
document.write( "p = what you want to find.<BR>\n" );
document.write( "r = .034 per year<BR>\n" );
document.write( "n = 29/12 years\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get p = 96,000 / e^(.034 * 29/12).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this gets you p = 88427.36891\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "converting interest rate per year to interest rate per month, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 96,000<BR>\n" );
document.write( "p = what you want to find.<BR>\n" );
document.write( "r = .034/12 per month<BR>\n" );
document.write( "n = 29 months\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get p = 96,000 / e^(.034/12 * 29)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this gets you p = 88427.36891\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "keeping the rate per time period and the number of time periods consistent is the key.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, first one gets you p = 80721 and second one gets you p = 88427.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "first one gets you the smaller present value.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );