document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088299>Question 1088299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #15: What lump sum deposited today at 12% compounded quarterly for 15 years will yield the same final amount as deposits of $5,000 at the end of each 6-month period for 15 years at 6% compounded semiannually? Round to the nearest cent as needed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702822 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=702822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question:<BR>\n" );
document.write( "What lump sum deposited today at 12% compounded quarterly for 15 years will yield the same final amount as deposits of $5,000 at the end of each 6-month period for 15 years at 6% compounded semiannually? Round to the nearest cent as needed.<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "Step 1:<BR>\n" );
document.write( "find the future value of $6000 deposited every 6 months for 15 years at APR=6%.<BR>\n" );
document.write( "A=6000<BR>\n" );
document.write( "n=2*15=30<BR>\n" );
document.write( "i=0.06/2=0.03<BR>\n" );
document.write( "F=A((1+i)^n-1)/i=6000(1.03^30-1)/0.03=285452.49\r<BR>\n" );
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document.write( "Step 2:<BR>\n" );
document.write( "Find present value of future $285452.49 if deposited at 12% compounded quarterly for 15 years.<BR>\n" );
document.write( "Convert future value to present value<BR>\n" );
document.write( "F=285452.49<BR>\n" );
document.write( "n=15*4=60<BR>\n" );
document.write( "i=0.12/4=0.03<BR>\n" );
document.write( "P=F(1+i)^n=285452.49/(1.03^60)=48450.73\r<BR>\n" );
document.write( "\n" );
document.write( "Answer: A deposit (present value) of 48450.73 at 12% compounded quarterly for 15 years will yield the same accumulated (future) value as $6000 deppsited at every 6 months earning 6% interest compounded every six months for 15 years.<BR>\n" );
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