document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996751>Question 996751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jason invested $5000 in a bank savings account which offered 4.75% p.a. simple interest that is paid every six months. At the end of the first year Jason discovered that he could obtain an interest rate of 4.5% p.a. compounded monthly. If he kept all the previous interest in his account, how much interest could he earn in the next 12 months using this interest rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615095 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=615095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> simple interest is paid on the original investment only.\r<BR>\n" );
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document.write( "it doesn't compound.\r<BR>\n" );
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document.write( "he invested 5000 at 4.75% per year simple interest that is paid every six months.\r<BR>\n" );
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document.write( "at the end of the first year his interest earned was .0475 * 5000 = 237.5\r<BR>\n" );
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document.write( "that was .0475 * 5000 / 2 = 118.75 for the first 6 months and the same amount for the second 6 months.\r<BR>\n" );
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document.write( "at the end of the year he had his original 5000 + 237.5 in interest for a total of 5237.5\r<BR>\n" );
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document.write( "he invests 5237.5 at 4.5% interest annually compounded monthly.\r<BR>\n" );
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document.write( "the monthly interests rate is .045/12 = .00375.\r<BR>\n" );
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document.write( "at the end of the second year he would have 5237.5 * 1.00375^12 = 5478.109834.\r<BR>\n" );
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document.write( "if he had kept the money in the simple interest account, he would have had 5000 + 2 * 237.5 = 5475.\r<BR>\n" );
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document.write( "he didn't make a lot more, but he did make more.\r<BR>\n" );
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document.write( "the difference becomes much greater the longer you keep the money invested.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "30 years at 4.75% per year on 5000 yields simple interest of 7125.\r<BR>\n" );
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document.write( "30 years at 4.5% per year on 5000 compounded monthly yields interest of 14238.\r<BR>\n" );
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