document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186455>Question 1186455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On her recent birthday, April 22, 2001, Nicole was given by her mother a certain sum of money as birthday present. She decided to invest the said amount on 20% exact simple interest. If the account will mature on Christmas day at an amount of P 10,000.00, How much did Nicole receive from her mother on her birthday </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849440 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the amount Nicole received from her mother:\r<BR>\n" );
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document.write( "1.  **Determine the time period:**<BR>\n" );
document.write( "    *   Nicole's birthday: April 22, 2001<BR>\n" );
document.write( "    *   Maturity date: December 25, 2020\r<BR>\n" );
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document.write( "    The time period is from April 22, 2001, to December 25, 2020. This is a span of 19 years, 8 months, and 3 days. In terms of exact simple interest, we count the exact number of days.\r<BR>\n" );
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document.write( "    From April 22, 2001 to December 25, 2020, there are 7164 days.\r<BR>\n" );
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document.write( "2.  **Use the simple interest formula:**<BR>\n" );
document.write( "    *   Future Value (FV) = Principal (P) + Interest (I)<BR>\n" );
document.write( "    *   Interest (I) = P * r * t<BR>\n" );
document.write( "    *   Where:<BR>\n" );
document.write( "        *   FV = Future Value (P 10,000.00)<BR>\n" );
document.write( "        *   P = Principal (what we want to find)<BR>\n" );
document.write( "        *   r = interest rate (20% or 0.20)<BR>\n" );
document.write( "        *   t = time in years (7164 days / 365 days/year ≈ 19.627 years)\r<BR>\n" );
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document.write( "3.  **Substitute and solve for P:**<BR>\n" );
document.write( "    *   FV = P + P * r * t<BR>\n" );
document.write( "    *   FV = P(1 + rt)<BR>\n" );
document.write( "    *   P = FV / (1 + rt)<BR>\n" );
document.write( "    *   P = 10,000 / (1 + (0.20 * 19.627))<BR>\n" );
document.write( "    *   P = 10,000 / (1 + 3.9254)<BR>\n" );
document.write( "    *   P = 10,000 / 4.9254<BR>\n" );
document.write( "    *   P ≈ 2029.92\r<BR>\n" );
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document.write( "Therefore, Nicole received approximately **P 2,029.92** from her mother on her birthday.<BR>\n" );
document.write( " </SPAN>\n" );
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