document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179711>Question 1179711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the periodic payments on the given loan or mortgage.<BR>\n" );
document.write( "$5,000,000 borrowed at 7% for 30 years, with quarterly payments<BR>\n" );
document.write( "PMT = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850182 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the quarterly payment for the loan:\r<BR>\n" );
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document.write( "**1. Given Information:**\r<BR>\n" );
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document.write( "* Principal (P): $5,000,000<BR>\n" );
document.write( "* Annual interest rate (r): 7% or 0.07<BR>\n" );
document.write( "* Loan term (t): 30 years<BR>\n" );
document.write( "* Compounding periods per year (n): 4 (quarterly)\r<BR>\n" );
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document.write( "**2. Calculate the Quarterly Interest Rate (i):**\r<BR>\n" );
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document.write( "* i = r / n = 0.07 / 4 = 0.0175\r<BR>\n" );
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document.write( "**3. Calculate the Total Number of Payments (N):**\r<BR>\n" );
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document.write( "* N = n * t = 4 * 30 = 120\r<BR>\n" );
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document.write( "**4. Use the Loan Payment Formula:**\r<BR>\n" );
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document.write( "PMT = P * [i * (1 + i)^N] / [(1 + i)^N - 1]\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* PMT = periodic payment<BR>\n" );
document.write( "* P = principal<BR>\n" );
document.write( "* i = interest rate per period<BR>\n" );
document.write( "* N = total number of payments\r<BR>\n" );
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document.write( "**5. Plug in the Values:**\r<BR>\n" );
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document.write( "PMT = 5000000 * [0.0175 * (1 + 0.0175)^120] / [(1 + 0.0175)^120 - 1]\r<BR>\n" );
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document.write( "PMT = 5000000 * [0.0175 * (1.0175)^120] / [(1.0175)^120 - 1]\r<BR>\n" );
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document.write( "**6. Calculate (1.0175)^120:**\r<BR>\n" );
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document.write( "(1.0175)^120 ≈ 7.612255\r<BR>\n" );
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document.write( "**7. Substitute and Solve:**\r<BR>\n" );
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document.write( "PMT = 5000000 * [0.0175 * 7.612255] / [7.612255 - 1]<BR>\n" );
document.write( "PMT = 5000000 * [0.1332144625] / [6.612255]<BR>\n" );
document.write( "PMT = 5000000 * 0.0201465<BR>\n" );
document.write( "PMT = 100732.5\r<BR>\n" );
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document.write( "**Answer:**\r<BR>\n" );
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document.write( "The quarterly payment (PMT) is approximately $100,732.50.<BR>\n" );
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