document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184696>Question 184696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need some help with part B. Also The answer I got for part A is $46,189.24. Is that correct? \r<BR>\n" );
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document.write( "You have $760,000 in your bank account.  The interest rate in your account is 5%.  Solve for the following:\r<BR>\n" );
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document.write( "a.  How much interest will you accumulate if interest is compounded  annually over the next five years?\r<BR>\n" );
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document.write( "b. How much interest will you earn in your account over the next five years with continuous compounding?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138619 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Part A.\r<BR>\n" );
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document.write( "Actually, you aren't even close.  Just do a quick mental sanity check.  10% of 760000 is 76000, so 5% is half of that or 38000.  If you only got 5% on your original principal and didn't compound you would get 5 times 38000 in 5 years -- nearly $200K.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  FV = P(1 + r)^n\">\r<BR>\n" );
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document.write( "Where <i>FV</i> is Future Value, <i>P</i> is Principal, <i>r</i> is the interest rate per compounding period, and <i>n</i> is the number of periods. \r<BR>\n" );
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document.write( "For your situation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  FV = 760000(1 + .05)^5 \approx 969973.99\">\r<BR>\n" );
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document.write( "(Said his calculator, confidently)\r<BR>\n" );
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document.write( "If the Future Value is $969,973.99 on an investment of $760,000.00, then the interest earned is the difference between the two or $209,973.99.\r<BR>\n" );
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document.write( "Part B.\r<BR>\n" );
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document.write( "Continuous compounding requires a different formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  FV = Pe^{rt}\">\r<BR>\n" );
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document.write( "Where <i>FV</i> is Future Value, <i>P</i> is Principal, <i>e</i> is the base of the natural logarithms (approx. 2.718), <i>r</i> is the interest rate per time period, and <i>t</i> is the number of time periods. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  FV = 760000\cdot e^{0.05\cdot5} \approx 975859.32\">\r<BR>\n" );
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document.write( "Again, subtracting the principal, the interest earned is: $215,859.32\r<BR>\n" );
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document.write( "So continuous compounding gets you an extra $100 per month over the 5 year period.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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