document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101888>Question 1101888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You need Rs 100000 to buy a new television <BR>\n" );
document.write( "If you have 6000 to invest at 5 percent compound anually how long you have to wait to buy the television </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716515 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=716515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the cost of the television is 100,000.\r<BR>\n" );
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document.write( "you have 6,000\r<BR>\n" );
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document.write( "the interest rate is 5% compounded annually.\r<BR>\n" );
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document.write( "the formula is f = p * (1+r) ^ n\r<BR>\n" );
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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 tiem period<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "f = 100,000<BR>\n" );
document.write( "p = 6,000<BR>\n" );
document.write( "r = .05<BR>\n" );
document.write( "n = what you want to find.\r<BR>\n" );
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document.write( "the formula becomes 100,000 = 6,000 * 1.05 ^ n\r<BR>\n" );
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document.write( "divide both sides of this formula by 6,000 to get 100,000 / 6,000 = 1.05 ^ n\r<BR>\n" );
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document.write( "simplify to get 100/6 = 1.05 ^ n\r<BR>\n" );
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document.write( "take the log of both sides of this equation to get:\r<BR>\n" );
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document.write( "log(100/6) = log(1.05 ^ n)\r<BR>\n" );
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document.write( "since log(1.05 ^ n) is equal to n * log(1.05), the equation becomes:\r<BR>\n" );
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document.write( "log(100/6) = n * log(1.05)\r<BR>\n" );
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document.write( "divide both sides of this equation by log(1.05) to get:\r<BR>\n" );
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document.write( "log(100/6) / log(1.05) = n\r<BR>\n" );
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document.write( "solve for n to get:\r<BR>\n" );
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document.write( "n = 57.66348125.\r<BR>\n" );
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document.write( "it would take 57.66348125 years for 6,000 rs to becomes 100,000 rs if you invest it at 5% per year compounded annually.\r<BR>\n" );
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document.write( "6,000 * 1.05 ^ (57.66348125) is equal to 100,000.\r<BR>\n" );
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document.write( "that's a life time.\r<BR>\n" );
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document.write( "perhaps you meant the cost of the television is 10,000 rs?\r<BR>\n" );
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document.write( "if that's the case, then the formula becomes:\r<BR>\n" );
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document.write( "10,000 = 6,000 * 1.05 ^ n\r<BR>\n" );
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document.write( "divide both sides by 6,000 and simplify to get 10/6 = 1.05 ^ n\r<BR>\n" );
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document.write( "take the log of both sides and simplify to get log(10/6) = n * log(1.05)\r<BR>\n" );
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document.write( "divide both sides by log(1.05) to get log(10/6) / log(1.05) = n\r<BR>\n" );
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document.write( "solve for n to get n = 10.46984843.\r<BR>\n" );
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document.write( "6,000 * 1.05 ^ 10.46984843 = 10,000.\r<BR>\n" );
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document.write( "if the cost of the television was 10,000 rs, it would take you 10.46984843 years for your invested amount of 6,000 rs to become equal to that.\r<BR>\n" );
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document.write( "you would still have to wait a very long time, but 10 years is certainly better than 57.\r<BR>\n" );
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