document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178093>Question 1178093</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rose makes an investment worth Php 15,000 in a savings bank paying 14% compounded monthly. If she withdraws all her investments and the interest with amounts to Php 19, 450,how long did she invest her money? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807249 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=807249\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula to use is f = p * (1 + r) ^ n<BR>\n" );
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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in your problem:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 19450<BR>\n" );
document.write( "p = 15000<BR>\n" );
document.write( "r = 14% / 100 = .14 / 12 = .01166666667 per month.<BR>\n" );
document.write( "n = the number of months you want to find.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula becomes 19450 = 15000 * (1 + .01166666667) ^ n\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of the equation by 15000 to get:<BR>\n" );
document.write( "19450/15000 = (1 + .01166666667) ^ n<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(19450/15000) = log((1 + .01166666667) ^ n)<BR>\n" );
document.write( "since log(x^n) = n * log(x), this becomes:<BR>\n" );
document.write( "log(19450/15000) = n * log(1.01166666667)<BR>\n" );
document.write( "divide both sides of the equation by log(1.01166666667) to get:<BR>\n" );
document.write( "log(19450/15000) / log(1.01166666667) = n<BR>\n" );
document.write( "solve for n to get:<BR>\n" );
document.write( "n = 22.39795036 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "confirm this is correct by replacing n in the original equation with that to get:<BR>\n" );
document.write( "f = 15000 * (1 + .01166666667) ^ 22.39795036 = 19450.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this confirms the solution is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the solution is 22.39795036 months for 15000 to grow to 19450 at 14% interest per year compounded monthly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you could also have used an online financial calculator to get the same results.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here are the inputs to that calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/040501.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here is the output from that calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/040502.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the calculator uses the percent rather than the rate.<BR>\n" );
document.write( "the calculator rounds the answer to 2 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );