document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104798>Question 1104798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a bank pays 2% compounded quarterly, how much should be deposited now to have $10,000\r<BR>\n" );
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document.write( "(a) 5 years later  (b) 10 years later </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719484 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=719484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2% per year / 100 = .02 per year interest rate.\r<BR>\n" );
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document.write( ".02 interest rate per year compounded quarterly is equal to .005 interest rate per quarter.\r<BR>\n" );
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document.write( "5 years * 4 quarters per year = 20 quarters.\r<BR>\n" );
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document.write( "10 years * 4 quarters peryear = 40 quarters.\r<BR>\n" );
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document.write( "your time period is quarters of a year.\r<BR>\n" );
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document.write( "the formula 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( "in your first problem:\r<BR>\n" );
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document.write( "p is what you want to find.<BR>\n" );
document.write( "f is equal to 10,000 dollars.<BR>\n" );
document.write( "r is equal to .005<BR>\n" );
document.write( "n is equal to 5.\r<BR>\n" );
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document.write( "formula becomes 10,000 = p * (1 + .005) ^ 20\r<BR>\n" );
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document.write( "divide both sides of this equation by (1 + .005) ^ 20 to get 10,000 / (1 + .005) ^ 20 = p\r<BR>\n" );
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document.write( "solve for p to get p = 9050.629043.\r<BR>\n" );
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document.write( "confirm by replacing p in the formula of f = p * (1 + r) ^ 20 to get f = 9050.629043 * (1 + .005) ^ 20.\r<BR>\n" );
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document.write( "solve for f to get f = 10,000, confirming the solution is good.\r<BR>\n" );
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document.write( "in your second problem, the formula of f = p * (1 + r) ^ n becomes:\r<BR>\n" );
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document.write( "10,000 = p * (1 + .005) ^ 40.\r<BR>\n" );
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document.write( "solve for p to get p = 10,000 / (1 + .005) ^ 40 = 8191.388607.\r<BR>\n" );
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document.write( "confirm by replacing p in the formula of f = p * (1 + r) ^ 40 to get f = 8191.388607 * (1 + .005) ^ 40.\r<BR>\n" );
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document.write( "solve for f to get f = 10,000, confirming the solution is correct.\r<BR>\n" );
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document.write( "if you are given the annual rate percent, you have to divide by 100 to get the annual rate.<BR>\n" );
document.write( "in this case 2% was divided by 100 to get .02.\r<BR>\n" );
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document.write( "you then divide the annual rate by the number of compounding periods per year to get the rate per compounding period.<BR>\n" );
document.write( "in this case .02 was divided by 4 to get a quarterly rate of .005.\r<BR>\n" );
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document.write( "you then take the number of years and multiply them by the number of compounding periods per year.<BR>\n" );
document.write( "in this case 5 years became 20 quarters and 10 years became 40 quarters.\r<BR>\n" );
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document.write( "your solution for (a) is 9050.629043\r<BR>\n" );
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document.write( "your solution for (b) is 8191.388607\r<BR>\n" );
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document.write( " </SPAN>\n" );
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