document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207430>Question 1207430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A property worth $35 OOO is purchased for 10% down and semi-annual payments of $2100 for 12 years. What is the nominal annual rate of interest if interest is compounded quarterly? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845291 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=845291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the amount of the loan is equal to .90 * 35000 = 31500.\r<BR>\n" );
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document.write( "for a 12 year loan, there are 24 semi-annual payments of 2100, made at the end of each semi-annual time period.\r<BR>\n" );
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document.write( "using the ti-business analyst 2 calculator, i get a semi-annual interest rate of 4.160152395%-\r<BR>\n" );
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document.write( "divide that by 100 and then add 1 to it to get a semi-annual growth factor of 1.04160152395.\r<BR>\n" );
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document.write( "raise that to the second power to get an effective annual growth factor of 1.084933735.\r<BR>\n" );
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document.write( "take the fourth root of that to get an effective quarterly growth factor of 1.020588812.\r<BR>\n" );
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document.write( "subtract 1 from that and then multiply it by 400 to get a nominal annual growth rate of 8.035524952%.\r<BR>\n" );
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document.write( "that should be your answer.\r<BR>\n" );
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document.write( "to see if this makes sense, do the following.\r<BR>\n" );
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document.write( "assume the nominal interest rate is what you just derived, meaning it is equal to 8.035524952%.\r<BR>\n" );
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document.write( "to find the quarterly interest rate, divide that by 4 to get 2.058881238%.\r<BR>\n" );
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document.write( "to convert that to a quarterly growth factor, divide it by 100 and then add 1 to it to get 1.02058881238.\r<BR>\n" );
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document.write( "raise that to the second power to get an effective semi-annual growth factor of 1.041601524.\r<BR>\n" );
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document.write( "subtract 1 from that and then multiply it by 100 to get 4.1601524%.\r<BR>\n" );
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document.write( "that's the same semi-annual interest rate that i got using the financial calculator, indicating that the quarterly growth factor is correct.\r<BR>\n" );
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document.write( "i'm reasonably sure that this is correct.<BR>\n" );
document.write( "your solution should be a nominal annual interest rate of 8.035524952%. which is equal to 8.0355% when rounded to 4 decimal places which is equal to 8.04% when rounded to 2 decimal places.\r<BR>\n" );
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document.write( "the financial calculator at <a  rel=nofollow HREF= \"\" target = \"_blank\"></a> can be used to find the semi-annual interest rate.\r<BR>\n" );
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document.write( "the result of that analysis is shown below:\r<BR>\n" );
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document.write( "the inputs were:\r<BR>\n" );
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document.write( "present value = 31500<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "number of time periods = 12 years * 2 time periods per year = 24 semi-annual time periods.<BR>\n" );
document.write( "the payments at the end of each time period are 2100, shown as -2100 because they are money going out.\r<BR>\n" );
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document.write( "click on interest rate % per time period and you get 4.160152%.\r<BR>\n" );
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document.write( "this agrees with that i got using the ti-business analyst 2 calculator, when rounding is taken into consideration.\r<BR>\n" );
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