document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133490>Question 1133490</A>: <I><SPAN STYLE=\"word-break: break-all;\">  If $100 invested at time 0 accumulates to $172 at time 3, find the accumulated value at time 10 of $100 invested at time 5. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750738 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=750738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you didn't specify whether it was compound interest or simple interest.\r<BR>\n" );
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document.write( "if it was compound interest, the formula is f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "n = time period 3 minus time period 0 = 3<BR>\n" );
document.write( "f = 172<BR>\n" );
document.write( "p = 100\r<BR>\n" );
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document.write( "formula becomes 172 = 100 * (1 + r) ^ 3\r<BR>\n" );
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document.write( "divide both sides of the equation by 100 and take the third root of both sides of the equation to get:\r<BR>\n" );
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document.write( "(172/100) ^ (1/3) = 1 + r\r<BR>\n" );
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document.write( "solve for r to get r = (172/100) ^ (1/3) - 1.\r<BR>\n" );
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document.write( "this makes r = .198145283.\r<BR>\n" );
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document.write( "that's the interest rate per time period.\r<BR>\n" );
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document.write( "f = 100 * (1.198145283) ^ 3 becomes f = 172.\r<BR>\n" );
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document.write( "the interest rate per time period is good.\r<BR>\n" );
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document.write( "time period 10 minus time period 5 = 5\r<BR>\n" );
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document.write( "100 invested in time period 5 at the same rate for 5 time periods makes the formula equal to:\r<BR>\n" );
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document.write( "f = 100 * (1.198145283) ^ 5 which makes f equal to 246.9149645.\r<BR>\n" );
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document.write( "the accumulated value at time period 10 is 246.9149645.\r<BR>\n" );
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document.write( "the formula for simple interest is:\r<BR>\n" );
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document.write( "i = p * r * n\r<BR>\n" );
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document.write( "i is the interest<BR>\n" );
document.write( "p is the principal<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time period.\r<BR>\n" );
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document.write( "the future value of the investment is f = p + i.<BR>\n" );
document.write( "since i = p * r * n, you get f = p + p * r * n.<BR>\n" );
document.write( "you can factor out the p to get f = p * (1 + r * n)\r<BR>\n" );
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document.write( "when p = 100 and f = 172 and n = 3, the formula becomes:\r<BR>\n" );
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document.write( "172 = 100 * (1 + r * 3)\r<BR>\n" );
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document.write( "divide both sides of the equation by 100 and subtract 1 from both sides of the equation and then divide both sides of the equation by 3 to get:\r<BR>\n" );
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document.write( "(172/100 - 1) / 3 = r\r<BR>\n" );
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document.write( "solve for r to get r = .24\r<BR>\n" );
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document.write( "the simple interest rate is .24 per time period.\r<BR>\n" );
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document.write( "the original equation for f is f = p + p * r * n<BR>\n" );
document.write( "that becomes f = 100 + 100 * .24 * 3 which becomes f = 172.\r<BR>\n" );
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document.write( "when n = 5, the formula becomes f = 100 + 100 * .24 * 5 which becomes f = 220.\r<BR>\n" );
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document.write( "with compound interest formula, the interest rate per time period is .198145283.<BR>\n" );
document.write( "in 3 years, 100 grows to 172.<BR>\n" );
document.write( "in 5 years, 100 grows to 246.9149645.\r<BR>\n" );
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document.write( "with simple interest formula, the interest rate per time period is .24.<BR>\n" );
document.write( "in 3 years, 100 grows to 172.<BR>\n" );
document.write( "in 5 years, 100 grows to 220.\r<BR>\n" );
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document.write( "compound interest formula graph is shown below followed by simple interest formula graph.\r<BR>\n" );
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document.write( "equation for compound interest graph is y = 100 * 1.198145283 ^ x\r<BR>\n" );
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document.write( "equation for simple interest graph is y = 100 + 100 * .24 * x\r<BR>\n" );
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document.write( "here's the graphs.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/012701.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/012702.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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