document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170595>Question 1170595</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Xian opened a savings account and put Php 6,250 in it. Each year, the account increases by 20%. How many years will it take the account to reach Php 12,960? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795445 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=795445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula to use if f = p * (1 + r) ^ n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = future value<BR>\n" );
document.write( "p = present value<BR>\n" );
document.write( "r = interest rate per time period.<BR>\n" );
document.write( "n = number of time periods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in your problem, the formula becomes 12,960 = 6,250 * (1 + .2) ^ n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the interest rate in the formula is equal to the interest rate percent divided by 100.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's why the interest rate per time period is equal to 20% / 100 = .2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you want to solve for n.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of the equation by 6,250 to get:<BR>\n" );
document.write( "12,960 / 6,250 = (1 + .2) ^ n<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(12,960 / 6,250) = log((1 + .2) ^ n)<BR>\n" );
document.write( "since log((1 + .2) ^ n) = n * log(1 + .2), the equation becomes:<BR>\n" );
document.write( "log(12,960 / 6,250) = n * log(1 + .2)<BR>\n" );
document.write( "divide both sides of the equation by log(1 + .2) to get:<BR>\n" );
document.write( "log(12,960 / 6,250) / log(1 + .2) = n<BR>\n" );
document.write( "solve for n to get:<BR>\n" );
document.write( "n = 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "confirm the solution is good by replacing n in the original equation to get:<BR>\n" );
document.write( "12,960 = 6,250 * (1 + .2) ^ 4<BR>\n" );
document.write( "solve to get:<BR>\n" );
document.write( "12,960 = 12960.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this confirms the solution is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );