document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198640>Question 1198640</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Twins graduate from college together and start their careers. Twin 1 invests $1500 at the end of each year for 10 years only (until age 31) in an account that earns 8%, compounded annually. Suppose that twin 2 waits until turning 40 to begin investing. How much must twin 2 put aside at the end of each year for the next 25 years in an account that earns 8% compounded annually in order to have the same amount as twin 1 at the end of these 25 years (when they turn 65)? (Round your answer to the nearest cent.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848290 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate the Future Value of Twin 1's Investments**\r<BR>\n" );
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document.write( "Twin 1 is making annual investments of $1500 for 10 years at an 8% annual interest rate. This is an ordinary annuity. \r<BR>\n" );
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document.write( "* **Future Value of Annuity:** <BR>\n" );
document.write( "    * FV = P * (((1 + r)^n) - 1) / r <BR>\n" );
document.write( "        * where:<BR>\n" );
document.write( "            * FV = Future Value<BR>\n" );
document.write( "            * P = Periodic Payment ($1500)<BR>\n" );
document.write( "            * r = Interest Rate per period (0.08)<BR>\n" );
document.write( "            * n = Number of periods (10 years)\r<BR>\n" );
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document.write( "* **Calculate FV for Twin 1:**<BR>\n" );
document.write( "    * FV = 1500 * (((1 + 0.08)^10) - 1) / 0.08 <BR>\n" );
document.write( "    * FV ≈ $21,729.84\r<BR>\n" );
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document.write( "**2. Calculate the Required Annual Investment for Twin 2**\r<BR>\n" );
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document.write( "Twin 2 needs to accumulate the same future value ($21,729.84) in 25 years with the same 8% interest rate.\r<BR>\n" );
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document.write( "* **Rearrange the Future Value of Annuity formula to solve for the periodic payment (P):**<BR>\n" );
document.write( "    * P = FV * (r / ((1 + r)^n) - 1))\r<BR>\n" );
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document.write( "* **Calculate the required annual investment for Twin 2:**<BR>\n" );
document.write( "    * P = 21729.84 * (0.08 / ((1 + 0.08)^25) - 1))<BR>\n" );
document.write( "    * P ≈ $297.24\r<BR>\n" );
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document.write( "**Therefore, Twin 2 needs to invest approximately $297.24 at the end of each year for the next 25 years to have the same amount of savings as Twin 1 at age 65.**<BR>\n" );
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