document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205437>Question 1205437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lady Lee needs TZS 57,500,000 at the end of the year 2029, and her only investment outlet is a 9 percent long term certificate of deposit from Puzzo Bank (compounded biannually). With the cectificate of deposit, she makes an initial investment at the beginning of the year 2023.<BR>\n" );
document.write( "1:What single payment could be made at the beginning of the year 2023 to achieve thi objective?<BR>\n" );
document.write( "W:What amount could Lady Lee invest at the end of each year annually up to the ye 2029 to achieve this same objective? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842239 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=842239\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> she needs 57,500,000 at the end of 2029.<BR>\n" );
document.write( "the initial investment is at the beginning of the year 2023.<BR>\n" );
document.write( "the interest rate is 9% compounded semi-annually.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the semi-annual interest rate is 9% divided by 2 = 4.5% every 6 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2029 minus 2023 = 6 years.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can use the calculator at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a> to solve these problems.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1: What single payment could be made at the beginning of the year 2023 to achieve this objective?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "future value = 57,500,000<BR>\n" );
document.write( "interest rate per semi-annual time period = 4.5%<BR>\n" );
document.write( "number of time periods = 6 years * 2 semi-annual time periods per year = 12 semi-annual time periods.<BR>\n" );
document.write( "payments per semi-annual time period = 0<BR>\n" );
document.write( "payments made at the end of each semi-annual time period is not used.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "calculator tells you that the present value needs to be 33,905,672.23.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's what it looks like on the calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/122012.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2: What amount could Lady Lee invest at the end of each year annually up to the year 2029 to achieve this same objective?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use the same calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "present value = 0<BR>\n" );
document.write( "future value = 57,500,000<BR>\n" );
document.write( "interest rate per annual time period = 9% per annual time period divided by 2 = 4.5% per semi-annual time period.<BR>\n" );
document.write( "that is divided by 100 to get .045 and then has 1 added to it to get 1.045 and then raised to the power of 2 to get 1.045^2 = 1.092025 and then has 1 subtracted from it to get .092025 multiplied by 100 = 9.2025% per annual time period.<BR>\n" );
document.write( "number of annual time periods = 6.<BR>\n" );
document.write( "payments are made at the end of each annual time period.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "calculator tells you that the payments made at the end of each annual time period = 7,603,935.46.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the interest rate is compounded semi-annually, the nominal interest rate of 9.0 is divided by 2 to get a semi-annual interest rate of 4.5%.<BR>\n" );
document.write( "that is then divided by 100 to get .045 and added to 1 to get 1.045 and raised to the power of 2 to get 1.045^2 = 1.092025.<BR>\n" );
document.write( "it then has 1 subtracted from it to bet .092025 and is then multiplied by 100 to get 9.2025%.<BR>\n" );
document.write( "that's the interest rate per annual time period used in the calculator for problem number 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's what it looks like in the calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/122011.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "le me know if you have any questions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "theo\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<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" );