document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139585>Question 1139585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Compute the future value after one year for $100 invested at 4% interest compounded quarterly. what simple interest rate will yield the same amount in one year </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760138 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=760138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for compound interest is f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "when you are compounding quarterly for 1 year, .....\r<BR>\n" );
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document.write( "r = 4% per year / 4 = 1% per quarter = .01\r<BR>\n" );
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document.write( "n = 1 year * 4 = 4 quarters.\r<BR>\n" );
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document.write( "the formula becomes f = 100 * (1 + .01) ^ 4 = 104.060401.\r<BR>\n" );
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document.write( "the interest earned is 104.060401 - 100 = 4.060401.\r<BR>\n" );
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document.write( "the simple interest rate is 4.060401 / 100 = .04060401.\r<BR>\n" );
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document.write( "that's a simple interest rate of .04060401 per year.\r<BR>\n" );
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document.write( "the simple interest formula is i = p * r * n\r<BR>\n" );
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document.write( "when dealing with quarters, the annual interest rate of .04060401 is divided by 4 to get a quarterly interest rate of .0101510025.\r<BR>\n" );
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document.write( "the simple interest formula becomes i = 100 * .0101510025 * 4.\r<BR>\n" );
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document.write( ".0101510025 is the interest rate per quarter and 4 is the number of quarters.\r<BR>\n" );
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document.write( "solve for i to get i = 100 * .0101510025 * r = 4.060401.\r<BR>\n" );
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document.write( "that's the same interest as we got using the compound interest formula.\r<BR>\n" );
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document.write( "this is as expected since we derived the simple interest rate formula from the results of the compound interest rate formula.\r<BR>\n" );
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document.write( "your solution is that the simple interest rate that will yield the same amount as was derived using the compound interest formula is .04060401.\r<BR>\n" );
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document.write( "a simple interest rate of .04060401 per year is equal to a simple interest rate of 4.060401% per year.\r<BR>\n" );
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document.write( "percent rate is divided by 100 to get rate.<BR>\n" );
document.write( "rate is multiplied by 100 to get percent rate.\r<BR>\n" );
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document.write( "if your answer is rate only, then .04060401.<BR>\n" );
document.write( "if you answer is rate percent, then 4.060401%.\r<BR>\n" );
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document.write( "that'a an annual interest rate.<BR>\n" );
document.write( "the quarterly simple interest would be that divided by 4.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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