document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189628>Question 1189628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a Php 25,000 investment receives 5% interest each year, after how many years will the investment have doubled in value </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821049 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "We use this compound interest formula<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "In this case,<BR>\n" );
document.write( "A = 50,000 = because we wish to double the deposit amount P<BR>\n" );
document.write( "P = 25,000 = principal or deposit amount<BR>\n" );
document.write( "r = 0.05 = interest rate in decimal form<BR>\n" );
document.write( "n = 1 = since we're compounding annually<BR>\n" );
document.write( "t = unknown\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So,<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "50000 = 25000*(1+0.05/1)^(1*t)<BR>\n" );
document.write( "50000/25000 = (1.05)^t<BR>\n" );
document.write( "2 = (1.05)^t<BR>\n" );
document.write( "Ln(2) = Ln( (1.05)^t )<BR>\n" );
document.write( "Ln(2) = t*Ln( 1.05 )<BR>\n" );
document.write( "t = Ln(2)/Ln(1.05)<BR>\n" );
document.write( "t = 14.206699 approximately<BR>\n" );
document.write( "t = 15 years\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It takes <font color=red>approximately 15 years</font> for the money to double.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note the rule of 72 says<BR>\n" );
document.write( "72/5 = 14.4<BR>\n" );
document.write( "which is fairly close to the 14.206699 value we got earlier.<BR>\n" );
document.write( "To use this rule, we simply divide the value 72 over the numeric form of the interest rate. We treat the \"5\" as is without the percent sign.<BR>\n" );
document.write( "For more info, check out this page<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.basic-mathematics.com/why-the-rule-of-72-works.html\">https://www.basic-mathematics.com/why-the-rule-of-72-works.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Other things to notice<BR>\n" );
document.write( "A(t) = 25000(1.05)^t<BR>\n" );
document.write( "A(14) = 49,498.29<BR>\n" );
document.write( "A(15) = 51,973.20<BR>\n" );
document.write( "which helps confirm that 14 years is just a bit shy of the goal of Php 50,000; while 15 years will get you over the hurdle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Once again, the final answer is <font color=red>approximately 15 years</font><BR>\n" );
document.write( "</font><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );