document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137623>Question 1137623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On January 1, 2000, $12,400 was deposited into an account that earns 2.55% interest compounded monthly. On January 1, 2010, $1,600 was deposited into the account and the bank changed the interest rate to 2.31% compounded monthly. <BR>\n" );
document.write( "On January 1, 2014, $3,800 was withdrawn from the account and the interest rate was lowered to 1.99% compounded monthly. <BR>\n" );
document.write( " a.) if no other deposits, withdrawals, or rate changes occur, how much money did the account have on January 1, 2020?  <BR>\n" );
document.write( " b.) Determine the total interest that was earned from January 1, 2000 to January 1, 2020?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755480 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=755480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> on january 1, 2000 you deposited 12400 earning 2.55% interest compounded monthly.\r<BR>\n" );
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document.write( "on january 1, 2010, you deposited 4600 earning 2.31% compounded monthly.\r<BR>\n" );
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document.write( "on january 1, 2014, you withdrew 3800 from the account and the interest rate was lowered to 1.99% compounded monthly.\r<BR>\n" );
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document.write( "from january 1, 2000 to january 1, 2010 is 10 years.\r<BR>\n" );
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document.write( "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( "your timer periods are months.\r<BR>\n" );
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document.write( "for the first segment between january 1, 2000 and january 1, 2010, you get:\r<BR>\n" );
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document.write( "p = 12400<BR>\n" );
document.write( "n = 10 * 12 = 120 months.<BR>\n" );
document.write( "r = 2.55% / 100 = .0255 / 12 = .002125\r<BR>\n" );
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document.write( "formula becomes f = 12400 * (1 + .002125) ^ 120 = 15997.39535.\r<BR>\n" );
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document.write( "on january 1, 2010, 1600 is added to this to get a total of 17597.39535.\r<BR>\n" );
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document.write( "from january 1, 2010 to january 1, 2014, this is invested at the rate of 2.31% compounded monthly.\r<BR>\n" );
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document.write( "f = p * (1 + r) ^ n becomes:\r<BR>\n" );
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document.write( "f = 17597.39535 * (1 + .0231/12) ^ (4 * 12) = 19299.16978.\r<BR>\n" );
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document.write( "on january 1, 2014, 3800 was withdrawn, leaving a balance of 15499.16978\r<BR>\n" );
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document.write( "this was invested from january 1, 2014 to january 1, 2020 at the annual rate of 1.99% compounded monthly.\r<BR>\n" );
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document.write( "f = p * (1 + r) ^ n becomes:\r<BR>\n" );
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document.write( "f = 15499.16978 * (1 + .0199/12) ^ (6 * 12) = 17463.05606.\r<BR>\n" );
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document.write( "if i did this right, that should be what's in the account on january 1, 2020.\r<BR>\n" );
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document.write( "i double checked through excel and it appears i did it right, at least if i did it right in excel.\r<BR>\n" );
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document.write( "i think that's probably the answer you're looking for.\r<BR>\n" );
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document.write( "the amount in the account on january 1, 2020 = 17463.05606.\r<BR>\n" );
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document.write( "the total interest earned would probably be calculated as follows:\r<BR>\n" );
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document.write( "on january 1, 2000 you deposited 12400.\r<BR>\n" );
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document.write( "on january 1, 2010, this grew to 15997.39535.\r<BR>\n" );
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document.write( "interest earned would be 15997.39535 minus 12400 = 3597.39535.\r<BR>\n" );
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document.write( "on january 1, 2010, you had 17597.39535 in the account which grew to 19299.16978 on january 1, 2014.\r<BR>\n" );
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document.write( "interest earned would be 19299.16978 minus 17597.39535 = 1701.77443.\r<BR>\n" );
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document.write( "on january 1, 2014, you had 15499.16978 which grew to 17463.05606 on january 1, 2020.\r<BR>\n" );
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document.write( "interest earned would be 17463.05606 minus 15499.16978 = 1963.88628.\r<BR>\n" );
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document.write( "total interest earned was 3597.39535 + 1701.77443 + 1963.88628 = 7263.05606\r<BR>\n" );
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document.write( "i double checked this number through excel and it appears it is correct.\r<BR>\n" );
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document.write( "your solution should be:\r<BR>\n" );
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document.write( "a.) if no other deposits, withdrawals, or rate changes occur, how much money did the account have on January 1, 2020? \r<BR>\n" );
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document.write( "the amount in the account should be 17463.05606.\r<BR>\n" );
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document.write( "b.) Determine the total interest that was earned from January 1, 2000 to January 1, 2020?\r<BR>\n" );
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document.write( "the total interest earned should be 7263.056055.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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