document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193768>Question 1193768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A P38,000 loan bears interest at 10% compounded semi-annually and is to be repaid in semi-annual payments of P2,000 each. <BR>\n" );
document.write( "a. How many semi-annual payments must be the debtor make?<BR>\n" );
document.write( "b. What smaller final payment should he make six months after the last payment of P2,000 is made?<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 #848598 by </B><A HREF=/tutors/aboutme.mpl?userid=proyaop><B>proyaop(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=proyaop><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a. Determine the Number of Semi-Annual Payments**\r<BR>\n" );
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document.write( "* **Find the effective semi-annual interest rate:** <BR>\n" );
document.write( "    * Semi-annual interest rate = (1 + Annual Interest Rate / Number of compounding periods per year)^(Number of compounding periods per year) - 1<BR>\n" );
document.write( "    * Semi-annual interest rate = (1 + 0.10 / 2)^(2) - 1 <BR>\n" );
document.write( "    * Semi-annual interest rate = 0.0525 or 5.25%\r<BR>\n" );
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document.write( "* **Use a financial calculator or spreadsheet software (like Excel or Google Sheets) to determine the number of payments.**\r<BR>\n" );
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document.write( "    * **In Excel, you can use the NPER function:** <BR>\n" );
document.write( "        * `=NPER(rate, pmt, pv, [fv], [type])`<BR>\n" );
document.write( "            * rate: Semi-annual interest rate (0.0525)<BR>\n" );
document.write( "            * pmt: Payment amount (-2000) <BR>\n" );
document.write( "            * pv: Present value (38000)<BR>\n" );
document.write( "            * fv: Future value (0, as the loan will be fully paid off) <BR>\n" );
document.write( "            * type: 0 for payments at the end of each period (default)\r<BR>\n" );
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document.write( "    * This will give you the number of semi-annual payments required to repay the loan.\r<BR>\n" );
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document.write( "**b. Calculate the Smaller Final Payment**\r<BR>\n" );
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document.write( "1. **Calculate the remaining balance after the last full payment of P2,000:**<BR>\n" );
document.write( "   * This involves calculating the remaining balance after the number of full payments determined in part (a). You can use the financial calculator or spreadsheet functions like `FV` (future value) to calculate the remaining balance after these payments.\r<BR>\n" );
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document.write( "2. **Calculate the interest accrued on the remaining balance:**<BR>\n" );
document.write( "   * Multiply the remaining balance by the semi-annual interest rate.\r<BR>\n" );
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document.write( "3. **Calculate the final payment:**<BR>\n" );
document.write( "   * Final payment = Remaining balance + Interest accrued on the remaining balance\r<BR>\n" );
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document.write( "**Note:**\r<BR>\n" );
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document.write( "* This approach provides a general framework for solving this type of loan repayment problem. <BR>\n" );
document.write( "* The specific calculations will require the use of financial tools or software.\r<BR>\n" );
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document.write( "Let me know if you'd like to explore the calculations using a specific financial calculator or spreadsheet software. <BR>\n" );
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