document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=724057>Question 724057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How much money must be deposited now in an account paying 8% annual interest, compounded quarterly, to have a balance of $1,000 after 10 years?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443570 by </B><A HREF=/tutors/aboutme.mpl?userid=Jstrasner><B>Jstrasner(112)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Jstrasner><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=Jstrasner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=443570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hey,\r<BR>\n" );
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document.write( "So for this one, we need to create a formula for calculating the amount. A normal compounded interest formula looks like this:\r<BR>\n" );
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document.write( "A = B ( 1 + r ) ^n \r<BR>\n" );
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document.write( "Where A is the ending amount of money, in this case $1000. B is the beginning amount of money, in this case x because we don't know. Little r is the rate, in this case .08 (or 8%). Little n is the number of years the money is in the bank, in this case 10 years. This would work, HOWEVER, the interest is compounded quarterly, which means 4 times a year. Therefore the formula is change to look like this:\r<BR>\n" );
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document.write( "A = B ( 1 + r/t ) ^ (n)(t) \r<BR>\n" );
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document.write( "Where everything is the same except that we divide the rate (r) by the number of times a year the interest is made (t) and then instead of just taking that amount to the exponent of n, we need to first multiply n by the number of times per year (t). So this is what this problem would look like:\r<BR>\n" );
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document.write( "$1,000 = x ( 1 + .08/4 ) ^ (10)(4) \r<BR>\n" );
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document.write( "First we solve what is in the parentheses:\r<BR>\n" );
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document.write( " 1 + .08/4 => 1 + .02 => 1.02 \r<BR>\n" );
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document.write( "Then we multiply the exponents together:\r<BR>\n" );
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document.write( " (10)(4) => 40 \r<BR>\n" );
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document.write( "Then we take 1.02 ^ 40 => 2.208... \r<BR>\n" );
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document.write( "Now we have to isolate the x so we can solve for it. In order to do this, we need to get rid of the 2.208 by dividing both sides by 2.208 :\r<BR>\n" );
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document.write( " $1000/2.208 = x (2.208)/2.208 => 452.8985..... = x \r<BR>\n" );
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document.write( "And now we have the answer.\r<BR>\n" );
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document.write( "If we deposit around $453 into a bank with compound interest of 8% quarterly, we will have $1000 after 10 years. \r<BR>\n" );
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document.write( "Again the answer is $453. \r<BR>\n" );
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document.write( "I hope this helps! </SPAN>\n" );
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