document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=563742>Question 563742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a person borrows $10000 and agrees to repay the loan in equal instalments over 20 years. interest is 12% per annum on any money owing\r<BR>\n" );
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document.write( "A) what is the amount of each repayment, if the repayment are made <BR>\n" );
document.write( "i) annually, ii) quarterly, iii) monthly, iv) weekly\r<BR>\n" );
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document.write( "B) which is the cheapest of the four methods of repayment in (A) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365105 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=365105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> person borrows $10,000<BR>\n" );
document.write( "pays back loan in equal installments.<BR>\n" );
document.write( "interest is 12% per year.<BR>\n" );
document.write( "amount of repayments if:<BR>\n" );
document.write( "annually = 1338.79<BR>\n" );
document.write( "quarterly = 331.12<BR>\n" );
document.write( "monthly = 110.11<BR>\n" );
document.write( "weekly = 25.39\r<BR>\n" );
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document.write( "total paid with each method is:<BR>\n" );
document.write( "annually = 1338.79 * 20 - 10000 = 16775.8<BR>\n" );
document.write( "quarterly = 331.12 * 20 * 4 - 10000 = 16489.6<BR>\n" );
document.write( "monthly = 110.11 * 20 * 12 - 10000 = 16426.4<BR>\n" );
document.write( "weekly = 25.39 * 20 * 52 - 10000 = 16405.6\r<BR>\n" );
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document.write( "the cheapest of the four methods is paying every week.<BR>\n" );
document.write( "this is because the balance goes down with each payment so the total interest paid becomes less.\r<BR>\n" );
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document.write( "here's an example:<BR>\n" );
document.write( "loan is 10000<BR>\n" );
document.write( "interest is 10% per year.<BR>\n" );
document.write( "loan is paid off in one year.\r<BR>\n" );
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document.write( "yearly payments<BR>\n" );
document.write( "each payment is 10100.<BR>\n" );
document.write( "balance is 10000 * 1.10 = 10100 at the end of the year.<BR>\n" );
document.write( "you make a payment of 10100 at the end of the year and the balance becomes 10100 - 10100 = 0.<BR>\n" );
document.write( "total interest paid is 1 * 10100 - 10000 = 100.\r<BR>\n" );
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document.write( "semi-annual payments.<BR>\n" );
document.write( "interest rate is 10% / 2 = 5% every 6 months.<BR>\n" );
document.write( "each payment is 5378.04878.<BR>\n" );
document.write( "balance is 10000 * 1.05 = 10500 at the end of 6 months.<BR>\n" );
document.write( "you make a payment of 5378.04878 at the end of 6 months and the balance becomes <BR>\n" );
document.write( "10500 - 5378.04878 = 5121.95122<BR>\n" );
document.write( "balance is 5121.95122 * 1.05 = 5378.04878 at the end of 12 months.<BR>\n" );
document.write( "you make a payment of 5378.04878 at the end of 12 months and the balance becomes 5378.04878 - 5378.04878 = 0<BR>\n" );
document.write( "total interest paid is equal to 2 * 5378.04878 - 10000 = 756.09756<BR>\n" );
document.write( "total interest is less because the interest rate is being applied to the remaining balance and the remaining balance becomes less after each payment.<BR>\n" );
document.write( "10% of 10000 = 100<BR>\n" );
document.write( "5% of 10000 = 500 and then 5% of 5121.95122 = 256.09756 for a total interest of 756.09756\r<BR>\n" );
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document.write( " </SPAN>\n" );
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