document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104295>Question 1104295</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jason received a loan of $9,000 at 6.75% compounded quarterly. He had to make payments at the end of every quarter for a period of 1 year to settle the loan \r<BR>\n" );
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document.write( "Calcu.ate the size of payments? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719112 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=719112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the loan was 6000 at 6.75% compounded quarterly.<BR>\n" );
document.write( "he had to make payments at the end of each quarter for a period of 1 year.\r<BR>\n" );
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document.write( "present value = 6000<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "r% = 6.75% / 4= 1.6875% per quarter.<BR>\n" );
document.write( "number of quarters = 1 year * 4 = 4 quarters.<BR>\n" );
document.write( "payment made at the end of each quarter.\r<BR>\n" );
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document.write( "using a financial calculator, the payments would need to be equal to 1563.810689 at the end of each quarter.\r<BR>\n" );
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document.write( "at the beginning of the year, the remaining balance of the loan is 6000.\r<BR>\n" );
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document.write( "at the end of the first quarter, the remaining balance of the loan would be equal to 6000 * (1 + .0675/4) - 1563.810689 = 4537.439311.\r<BR>\n" );
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document.write( "at the end of the second quarter, the remaining balance of the loan would be equal to 4537.439311 * (1 + .0675/4) - 1563.810689 = 3050.197911.\r<BR>\n" );
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document.write( "at the end of the third quarter, the remaining balance of the loan would be equal to 3050.197911 * (1 + .0675/4) - 1563.810689 = 1537.859313.\r<BR>\n" );
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document.write( "at the end of the fourth quarter, the remaining balance of the loan would be equal to 1537.859313 * (1 + .0675/4) - 1563.810689 = 0.\r<BR>\n" );
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document.write( "the calculators usually work on percent, while the manual formulas usually work on the rate, which is the percent divided by 100.\r<BR>\n" );
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document.write( "if you need the manual formula to calculate the payment, that formula would be as shown below:\r<BR>\n" );
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document.write( "ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS \r<BR>\n" );
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document.write( "a = (p*r)/(1-(1/(1+r)^n)) \r<BR>\n" );
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document.write( "a is the annuity.<BR>\n" );
document.write( "p is the present amount.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods. \r<BR>\n" );
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document.write( "annuity and payment mean the same thing for this formula.\r<BR>\n" );
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document.write( "in your problem, the formula becomes a = (6000 * .0675/4) / (1 - (1 / (1 + .0675/4) ^ 4))\r<BR>\n" );
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document.write( "put the expression in your calculator exactly as shown and you get a = 1563.810689.\r<BR>\n" );
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document.write( "this is the same as the solution that the calculator gave me.\r<BR>\n" );
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document.write( "the calculator i used is the TI-BA Plus.<BR>\n" );
document.write( "BA stands for business analyst.\r<BR>\n" );
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document.write( "other financial formula you might find useful can be found here:\r<BR>\n" );
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