document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=565397>Question 565397</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Every £1 of money invested in a savings scheme continuously gains interest at a rate of 4% per year. Hence, after x years, the total value of an initial£1 investment is £y, where y = 1.04^x.\r<BR>\n" );
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document.write( "(a) Calculate, to the nearest £, the total value of an initial £800 investment after 10 years ?\r<BR>\n" );
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document.write( "(b) Use logarithms to find the number of years it takes to double the total value of any initial investment ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365781 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=365781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Every £1 of money invested in a savings scheme continuously gains interest at a rate of 4% per year. Hence, after x years, the total value of an initial£1 investment is £y, where y = 1.04^x.<BR>\n" );
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document.write( "(a) Calculate, to the nearest £, the total value of an initial £800 investment after 10 years ?<BR>\n" );
document.write( "A(10) = 800*1.04^10 = $1184.20<BR>\n" );
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document.write( "(b) Use logarithms to find the number of years it takes to double the total value of any initial investment ?<BR>\n" );
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document.write( "Solve: 2 = 1*1.04^x<BR>\n" );
document.write( "1.04^x = 2<BR>\n" );
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document.write( "x(log(1.04) = log(2)<BR>\n" );
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document.write( "x = log(2)/log(1.04) <BR>\n" );
document.write( "x = 17.67 years<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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