document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104576>Question 1104576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Derek used his credit card to buy a hay ride for him and his friends. The ride cost $500 plus 5% GST. He did not pay his bill within the grace period and must pay interest on his bill. The interest rate is 15% compounded daily from the date of purchase. \r<BR>\n" );
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document.write( "A) What is the total amount of hay ride with taxes? \r<BR>\n" );
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document.write( "B) At $120 per month, how long will it take Derek to pay off the balance? \r<BR>\n" );
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document.write( "C) How much will he pay in interest, paying $120 monthly?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720271 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=720271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the cost of the hay ride is 500.<BR>\n" );
document.write( "general sales tax is 5%.<BR>\n" );
document.write( "the total cost is 500 + .05 * 500 = 525.\r<BR>\n" );
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document.write( "he pays 120 at the end of each month until the debt is eliminated.\r<BR>\n" );
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document.write( "i calculate that it will take him 4.528196438 months to pay it off.\r<BR>\n" );
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document.write( "the interest rate is compounded daily and the payments are made monthly.\r<BR>\n" );
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document.write( "i used the TI Business Analyst II.\r<BR>\n" );
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document.write( "i assumed 365 days in a year.\r<BR>\n" );
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document.write( "using that calculator, i set P/Y = 12 and C/Y = 365\r<BR>\n" );
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document.write( "P/Y is payments per year.<BR>\n" );
document.write( "C/Y is compounding periods per year.\r<BR>\n" );
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document.write( "i then made the following entries.\r<BR>\n" );
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document.write( "PV = 525<BR>\n" );
document.write( "PMT = -120<BR>\n" );
document.write( "FV = 0<BR>\n" );
document.write( "I/Y = 15%\r<BR>\n" );
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document.write( "i then had the calculator tell me the number of months.\r<BR>\n" );
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document.write( "the calculator came back and said that the number of months required to pay off the loan was 4.528196438.\r<BR>\n" );
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document.write( "i then verified with the nper function of excel by entering the following:\r<BR>\n" );
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document.write( "rate = (1 + .15/365)^(365/12) - 1<BR>\n" );
document.write( "pv = 525<BR>\n" );
document.write( "pmt = -120<BR>\n" );
document.write( "fv = 0<BR>\n" );
document.write( "payments made at the end of the time period.\r<BR>\n" );
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document.write( "i got the same answer.\r<BR>\n" );
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document.write( "i'm not sure whether this answer will satisfy your requirements because the answer depends heavily on the assumptions used, but this is a reasonable answer as best as i can determine.\r<BR>\n" );
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document.write( "the number of months required is slightly more than if you used monthly compounding.\r<BR>\n" );
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document.write( "with monthly compounding, the number of months required came out to be 4.527239105.\r<BR>\n" );
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document.write( "with daily compounding, the number of months required came out to be 4.528196438.\r<BR>\n" );
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document.write( "the equivalent monthly interest rate for monthly compounding was .15/12 = .0125\r<BR>\n" );
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document.write( "the equivalent monthly interest rate for daily compounding was (1+ .15/365)^(365/12) - 1 = .012575851.\r<BR>\n" );
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document.write( "the use of a calculator that allows you to do compounding periods different from payment periods is recommended.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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