document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206582>Question 1206582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q;A loan of $ 10,000 is amortized by equal annual payments for 30 years at an effective annual interest rate of 13 %. Determine the year in which the interest portion of the payment is most nearly equal to one-third of the payment.<BR>\n" );
document.write( "How do i find the interest portion of the payment most nearly equal to 1/3 of the payment.\r<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 #844143 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=844143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the effective annual interest rate is 13%.\r<BR>\n" );
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document.write( "if you want the interest part of the payment to be equal to 1/3 the payment, you have to first find the payment.\r<BR>\n" );
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document.write( "i used the calculator at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a> to find the payment.\r<BR>\n" );
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document.write( "input to the calculator was:<BR>\n" );
document.write( "present value = -10000<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "number of time periods = 10 years<BR>\n" );
document.write( "interest rate per time period = 13% per year<BR>\n" );
document.write( "paments are made at the end of each time period.\r<BR>\n" );
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document.write( "the calculator tells me that the payment required at the end of each year is equal to 1842.90.\r<BR>\n" );
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document.write( "if you want the interest part of the payment to be equal to 1/3 the payment, then the interest part of the payment needs to be equal to 1/3 * 1842.90 = 614.30\r<BR>\n" );
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document.write( "that will occur when the remaining balance on the loan is equal to 614.3 / .13 = 4725.39, or the remaining balance closest to that.\r<BR>\n" );
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document.write( "i used excel to get the remaining balance at the end of each year, along with the interest part of the payment and the equity part of the payment.\r<BR>\n" );
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document.write( "excel gives an end of year account for each of the 10 years.\r<BR>\n" );
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document.write( "the formula used is remaining balance for the year is the remaining balance for the previous year * 1.13 minus the payment for the year.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "end of year 6 remaining balance is 5481.64.<BR>\n" );
document.write( "end of year 7 remaining balance is 5481.64 * 1.13 minus 1842.90 = 4351.36.\r<BR>\n" );
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document.write( "you only see the numbers rounded to the nearest penny.<BR>\n" );
document.write( "the calculations are done with the actual numbers stored that are not rounded to the nearest penny.\r<BR>\n" );
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document.write( "the end of year remaining balance closest to 4725 is the remaining balance for end of year 7, which is 4351.36.\r<BR>\n" );
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document.write( "the interest on that remaining balance is taken out as part of the payment for end of year 8.\r<BR>\n" );
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document.write( "that interest was calculated as 4351.36 * .13 = 565.68.\r<BR>\n" );
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document.write( "since they asked for the year in which the interest portion of the payment was most equal to 1/3 the payment, i would have to say that would be year 8.\r<BR>\n" );
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