document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140258>Question 1140258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long​ (in years) will it take Michael Garbin to pay off a ​$3000 loan with monthly payments of ​$154.95 if the​ add-on interest rate is 7.8​%? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760800 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=760800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> an add-on interest type loan adds the interest up front to the principal and then both the principal and the interest have to be payed off.\r<BR>\n" );
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document.write( "in your loan.\r<BR>\n" );
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document.write( "the principal is 3000<BR>\n" );
document.write( "the yearly interest rate is .078<BR>\n" );
document.write( "the monthly interest rate is .078 / 12 = .0065\r<BR>\n" );
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document.write( "looking at the possible number of month for your loan, assuming the loan is for a specified number of months, i don't get any number of months for the loan that would result in a payment of 154.95 a month.\r<BR>\n" );
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document.write( "the closest i get is for a 22 month loan.\r<BR>\n" );
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document.write( "my calculations for that loan would be:\r<BR>\n" );
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document.write( "3000 + .0065 * 3000 * 22 = 3429 / 22 = 155.8636364 per month.\r<BR>\n" );
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document.write( "that says that the number of months has to be between 22 and 23, based on your monthly payment figures.\r<BR>\n" );
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document.write( "i'm assuming, of course, that the payment per month would be the payment for the principal of 3000 plus the interest on that principal since that is how add-on interest loans are paid off.\r<BR>\n" );
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document.write( "this tells me that the 154.95 per month is to pay off the principal plus the interest for the number of months of the loan.\r<BR>\n" );
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document.write( "i then looked to derive a formula to determine the exact number of months required to pay off the loan.\r<BR>\n" );
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document.write( "my formula was:\r<BR>\n" );
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document.write( "n = 3000 / (mp - .0065 * 3000).\r<BR>\n" );
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document.write( "n represents the number of months required to pay off the loan.<BR>\n" );
document.write( "mp equals the monthly payment.\r<BR>\n" );
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document.write( "i then checked this out for loans that i knew the number of months and the monthly payment for.\r<BR>\n" );
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document.write( "for example, on a 24 month loan, the monthly payment would be 144.5.\r<BR>\n" );
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document.write( "based on that the formula becomes:\r<BR>\n" );
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document.write( "n = 3000 / (144.5 - .0065 * 3000) = 24\r<BR>\n" );
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document.write( "this told me the formula is accurate and will help me to determine the exact number of months for your loan.\r<BR>\n" );
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document.write( "since your monthly payment is 154.95, the formula becomes:\r<BR>\n" );
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document.write( "n = 3000 / (154.95 - .0065 * 3000) = 22.14839424\r<BR>\n" );
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document.write( "that tells me that the number of months required to repay your loan with a payment of 154.95 per month would be equal to 22.14839424.\r<BR>\n" );
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document.write( "since 22.14849424 months is between 22 and 23, that checks out with my previous analysis that assumed it has to be between 22 and 23 months.\r<BR>\n" );
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document.write( "22.14839424 months / 12 = 1.84569952 years.\r<BR>\n" );
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document.write( "that says that the number of years to required pay off your loan is equal to 1.84569952 years, based on a payment of 154.95 per month.\r<BR>\n" );
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document.write( "i don't know where the 154.95 came from, but using that value as the monthly payment does not allow me to come up with a number of months that is an integer.\r<BR>\n" );
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document.write( "here's a link to an add-on interest loan calculator that you might find useful.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.csgnetwork.com/addonintcalc.html\" target = \"_blank\">http://www.csgnetwork.com/addonintcalc.html</a>\r<BR>\n" );
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document.write( "here's a reference on add-on interest type loans.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.investopedia.com/terms/a/add-on_interest.asp\" target = \"_blank\">https://www.investopedia.com/terms/a/add-on_interest.asp</a> </SPAN>\n" );
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