document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172981>Question 1172981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Truth in Lending Law requires all lending institutions to fully disclose interest rates on all loans.  \r<BR>\n" );
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document.write( "$5000 is loaned for 36 months with monthly payments of $162.50.  Determine annual interest rate.\r<BR>\n" );
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document.write( "Not sure how to continue. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850793 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</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=850793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To determine the annual interest rate for this loan, we'll need to use a financial calculator or spreadsheet software because this calculation involves finding the interest rate that satisfies the loan payment formula.\r<BR>\n" );
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document.write( "Here's how we can approach it:\r<BR>\n" );
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document.write( "**1. Understand the Loan Details:**\r<BR>\n" );
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document.write( "* Principal (P): $5,000<BR>\n" );
document.write( "* Number of Payments (n): 36 months<BR>\n" );
document.write( "* Monthly Payment (PMT): $162.50\r<BR>\n" );
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document.write( "**2. Use the Loan Payment Formula (or a Financial Calculator/Spreadsheet):**\r<BR>\n" );
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document.write( "The loan payment formula is:\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 = Monthly payment<BR>\n" );
document.write( "* P = Principal loan amount<BR>\n" );
document.write( "* i = Monthly interest rate<BR>\n" );
document.write( "* n = Number of payments\r<BR>\n" );
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document.write( "We need to solve for 'i'. This is difficult to do algebraically, so we'll use a financial calculator or spreadsheet function.\r<BR>\n" );
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document.write( "**3. Using a Financial Calculator or Spreadsheet (Excel, Google Sheets):**\r<BR>\n" );
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document.write( "* **Financial Calculator:**<BR>\n" );
document.write( "    * Input the following:<BR>\n" );
document.write( "        * n = 36<BR>\n" );
document.write( "        * PV = 5000<BR>\n" );
document.write( "        * PMT = -162.50 (Note: PMT is negative because it's a cash outflow)<BR>\n" );
document.write( "        * FV = 0<BR>\n" );
document.write( "        * CPT I/Y (or I/YR)<BR>\n" );
document.write( "    * The result will be the monthly interest rate. Multiply it by 12 to get the annual rate.<BR>\n" );
document.write( "* **Excel/Google Sheets:**<BR>\n" );
document.write( "    * Use the `RATE` function:<BR>\n" );
document.write( "        * `=RATE(nper, pmt, pv, [fv], [type], [guess])`<BR>\n" );
document.write( "        * `=RATE(36, -162.50, 5000)`<BR>\n" );
document.write( "    * This will give you the monthly interest rate. Multiply it by 12 to get the annual rate.\r<BR>\n" );
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document.write( "**4. Calculation**\r<BR>\n" );
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document.write( "Using the rate function in excel, the monthly rate is approximately 0.0125, or 1.25%.\r<BR>\n" );
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document.write( "1.25% * 12 = 15%\r<BR>\n" );
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document.write( "**Result:**\r<BR>\n" );
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document.write( "The annual interest rate is approximately 15%.<BR>\n" );
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