document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476060>Question 476060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is the question:  Rule of 72 (Refer to Exercise 87 in Section 1.3.)<BR>\n" );
document.write( "If an investment of $25,000 earns 9% annual interest,<BR>\n" );
document.write( "approximate the value of the investment after<BR>\n" );
document.write( "24 years.\r<BR>\n" );
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document.write( "Rule of 72 Investors sometimes use the rule of 72<BR>\n" );
document.write( "to determine the time required to double an investment.<BR>\n" );
document.write( "If 72 is divided by the annual interest rate earned<BR>\n" );
document.write( "on an investment, the result approximates the number<BR>\n" );
document.write( "of years needed to double the investment. For example,<BR>\n" );
document.write( "an investment earning 6% annual interest will double<BR>\n" );
document.write( "in value approximately every 72  6  12 years. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326943 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=326943\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a 9% interest rate the Rule of 72 tells you that an investment will double in 8 years because 72/9 = 8.<BR>\n" );
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document.write( "Since the original investment was $25,000 it will double to $50,000 in 8 years. Now you are starting with $50,000 and since the interest rate remains at 9%, the $50,000 will double to $100,000 in the next 8 years.  Up to this point your original investment of $25,000 has grown to be $100,000 in a total of 16 years.<BR>\n" );
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document.write( "So at 16 years your $100,000 remains invested at 9%. It will again double in 8 more years. At that time the $100,000 doubles to $200,000 in 8 years. This added 8 year period makes the total investment period 24 years (16 + 8).<BR>\n" );
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document.write( "In summary your original investment of $25,000 grows to $200,000 in 24 years if it is invested at 9% and is left untouched.<BR>\n" );
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document.write( "A way of looking at this is that you double money every 8 years so that in 24 years you double, double again, and double one more time. This is 2*2*2 = 8 so that your original investment grows by 8 times (8 times $25,000 = $200,000).<BR>\n" );
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document.write( "Hope this helps you to understand the Rule of 72.  It's more useful when the interest rates are higher than banks are paying at present.  If you deposit money at 1% it will take 72 years (72/1) to double your money, whereas in this problem you doubled your money every 8 years.   </SPAN>\n" );
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