document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119011>Question 1119011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company invests 10,000 today to be repaid in five years in one lump sum at 12% compounded annually. If the rate of inflation is 3% compounded annually, how much profit in present day is realized over five years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734550 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=734550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the composite rate will be 1.12 / 1.03, if i remember correctly.\r<BR>\n" );
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document.write( "your money is earning at 12% per year, but the price of goods and services you can buy with it is increasing by 3% per year.\r<BR>\n" );
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document.write( "consequently, the value of your money, in terms of what it can buy today, is increasing at the composite rate of 1.12 / 1.03 = (1.087378641 - 1) * 100% = 8.7378641% per years.\r<BR>\n" );
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document.write( "your 10,000 invested at 12% per year for 5 years would be worth 10,000 * 1.12^5 = 17,623.41683 in 5 years, if you don't take into account inflation.\r<BR>\n" );
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document.write( "with inflation, your 10,000 invested at 12% per year for 5 years would be worth 10,000 * 1.12^5 / 1.03^5 = 15,202.11417 in 5 years in terms of today's purchasing power.\r<BR>\n" );
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document.write( "how does this work?\r<BR>\n" );
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document.write( "you have 10,000 and it can buy 10,000 worth of goods and services today.\r<BR>\n" );
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document.write( "the purchasing power of your 10,000 today is 10,000 / 10,000 = 1 times as much as it is today.\r<BR>\n" );
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document.write( "you invest your money at 12% per year for 5 years.<BR>\n" );
document.write( "it is worth 10,000 * 1.12 ^ 5 = 17623.41683 in 5 years.<BR>\n" );
document.write( "if you buy the same amount of goods and services and the price of them didn't change, then you could buy 17623.41683 / 10,000 = 1.762341683 times the amount of goods and services as you could buy today.\r<BR>\n" );
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document.write( "however, because of inflation, the price of the goods and services increased by 3% per year.<BR>\n" );
document.write( "the price 5 years from now is 10,000 * 1.03^5 = 11592.74074 dollars.<BR>\n" );
document.write( "when you buy the same amount of goods and services in 5 years, you can buy 17623.41683 / 11592.74074 = 1.520211417 times the amount of goods and services as you could buy today.\r<BR>\n" );
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document.write( "your increase in purchasing power, in terms of today's dollars is equal to 1.12 ^ 5 / 1.03 ^ 5 = 1.520211417 as much as it is today.\r<BR>\n" );
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document.write( "1.12^5 / 1.03^5 is equal to (1.12/1.03)^5 which is equal to the composite rate of 1.087378641 ^ 5.\r<BR>\n" );
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document.write( "bottom line:\r<BR>\n" );
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document.write( "your composite investment rate is equal to the pure investment rate divided by the inflation rate.\r<BR>\n" );
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document.write( "in your problem, the future purchasing power of your money, in today's dollars, is equal to 10,000 * (1.12/1.03)^5 = 15,202.11417.\r<BR>\n" );
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document.write( "your profit is equal to (15,202.11417 - 10,000) / 10,000 = .520211417, or 52.02% rounded to 2 decimal places.\r<BR>\n" );
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document.write( "to find the composite interest rate per year, you take 1 plus the investment rate and divide it by 1 plus the inflation rate.\r<BR>\n" );
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document.write( "1.12 / 1.03 = 1.087378641 which is a composite rate of 8.7378641% per year, taking into account inflation.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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