document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207545>Question 1207545</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For her daughter's university education, Carla Hackl has invested an inheritance in a fund paying 9.2% compounded quarterly. If ordinary annuity payments of $4750.00 per month are to be made out of the fund for 5 years and the annuity begins 7.75 years from now, how much was the inheritance? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845523 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=845523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> for this problem, i used the financial calculator at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the interest rate used is 9.2% per year compounded quarterly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that becomes 9.2/4 = 2.3% per quarter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equivalent monthly rate is 1.023 ^ (1/3) = 1.007608629, minus 1, * 100, = .7608628613%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both the quarterly rate and the monthly rate provide the same effective annual rate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1.023 ^ 4 = 1.095222948<BR>\n" );
document.write( "1.00768629 ^ 12 = the same.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the inheritance fund is invested into a fund that provides an interest rate of 9.2% per year compounded quarterly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "after 7.75 years, the money will then be invested into an ordinary annuity that provides 4750 at the end of each month for 5 years, presumably at the same interest rate compounded quarterly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the first thing that needs to be done is to find the present value of the annuity fund.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "inputs to the calculator for this part of the problenm are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "present value = 0<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "number of time periods = 5 * 12 = 60<BR>\n" );
document.write( "interest rate per time period = .7608628613%<BR>\n" );
document.write( "payment at the end of each time period = 4750.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "click on present value and calculator says that the present value is equal to 228,127.63.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the amount that needs to be invested in the ordinary annuity 7.75 years from the time the inheritance was received.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "7.75 years * 4 quarters per year = 31 quarters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the present value of that will be 228,127.63 / 1.023 ^ 31 = 112,728.37.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the amount of the inheritance, assuming the inheritance was just enough to provide for the investment that eventually proviced 4750 at the end of each month for 5 years.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "working back up to when the ordinary investment fund was investred, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "112,728.37 * 1.023 ^ 31 = 228,127.63 which is the present value of the ordinary annuity fund.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i would like to point out that i used the same interest rate and the same compounding rate because no other rates were provided for the ordinary income fund.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if that is not the case, then you need to go back to your instructor and find out what rate and compounding rate was to be used for the ordinary income fund.<BR>\n" );
document.write( "if it is different, then it will change the present value of that fund which will change the present value of the inheritance fund.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "with no changes, the present value of the inheritance is calculate to be 112,728.37.<BR>\n" );
document.write( "that should be your answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here are the results from the calculator used.<BR>\n" );
document.write( "the first found the present value of the ordinary income fund.<BR>\n" );
document.write( "the second found the present value of that from 7.75 years in the future.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/062002.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/062003.jpg\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );