document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199180>Question 1199180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider a student loan of $22,500 at a fixed APR of 12% for 25 years<BR>\n" );
document.write( "A.Calculate the monthly payment<BR>\n" );
document.write( "B.Determine the total amount paid over the term of the loan<BR>\n" );
document.write( "C. Of the total amount paid what percentage is paid towards the principal and what is percentage is paid interest  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832929 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832929\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (A)\r<BR>\n" );
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document.write( "Monthly payment formula<BR>\n" );
document.write( "P = (L*i)/( 1 - (1+i)^(-n) )<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "L = loan amount<BR>\n" );
document.write( "i = monthly interest rate in decimal form<BR>\n" );
document.write( "n = number of months\r<BR>\n" );
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document.write( "In this problem:<BR>\n" );
document.write( "L = 22500<BR>\n" );
document.write( "i = 0.12/12 = 0.01<BR>\n" );
document.write( "n = 25*12 = 300 months (equivalent to 25 years)\r<BR>\n" );
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document.write( "Let's find the monthly payment<BR>\n" );
document.write( "P = (L*i)/( 1 - (1+i)^(-n) )<BR>\n" );
document.write( "P = (22500*0.01)/( 1 - (1+0.01)^(-300) )<BR>\n" );
document.write( "P = 236.975431994467<BR>\n" );
document.write( "P = 236.98<BR>\n" );
document.write( "The monthly payment is $236.98\r<BR>\n" );
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document.write( "Verifying this result:\r<BR>\n" );
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document.write( "You can use a TVM solver such as this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.geogebra.org/m/mvv2nus2\">https://www.geogebra.org/m/mvv2nus2</a><BR>\n" );
document.write( "which emulates the TVM solver in a TI83 and TI84.\r<BR>\n" );
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document.write( "The inputs will be:<BR>\n" );
document.write( "N = 300<BR>\n" );
document.write( "I% = 12<BR>\n" );
document.write( "PV = 22500<BR>\n" );
document.write( "PMT = left blank or set to whatever you want<BR>\n" );
document.write( "FV = 0<BR>\n" );
document.write( "P/Y = 12<BR>\n" );
document.write( "C/Y = 12<BR>\n" );
document.write( "Do not type dollar signs or commas into any of the boxes.\r<BR>\n" );
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document.write( "Here's an explanation of each input:<ul><li>N = number of months in this case</li><li>I% = annual interest rate in percent form (not decimal form)</li><li>PV = present value, aka starting balance, aka loan amount</li><li>FV = 0 since we want the future value of the loan, aka final balance, to be $0 when it's all paid off</li><li>P/Y = 12 means there are 12 payments per year</li><li>C/Y = 12 means there are 12 compounding periods per year</li></ul>After the items are filled into the proper boxes, press the \"Solve for PMT\" button to have -236.98 show up in that box.<BR>\n" );
document.write( "This value is negative to represent a cash outflow.\r<BR>\n" );
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document.write( "Here is another free online calculator you can use to verify the monthly payment:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.calculator.net/loan-calculator.html\">https://www.calculator.net/loan-calculator.html</a><BR>\n" );
document.write( "There are many other options as well.\r<BR>\n" );
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document.write( "Part (B)\r<BR>\n" );
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document.write( "The monthly payment is $236.98 found in part (A).<BR>\n" );
document.write( "It is done for 300 months (aka 25 years)<BR>\n" );
document.write( "This assumes no refinancing is done.\r<BR>\n" );
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document.write( "300*236.98 = 71,094\r<BR>\n" );
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document.write( "Therefore, a total of $71,094 is paid back.\r<BR>\n" );
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document.write( "Part (C)\r<BR>\n" );
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document.write( "The previous part found that $71,094 was paid back in total.<BR>\n" );
document.write( "This consists of principal, aka the amount loaned, and interest.\r<BR>\n" );
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document.write( "Divide the loan amount over this total paid back<BR>\n" );
document.write( "22500/71094 = 0.31648 = 31.648% approximately<BR>\n" );
document.write( "This is the percentage of the total paid toward principal.\r<BR>\n" );
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document.write( "The remaining 100% - 31.648% = 68.352% is paid toward interest.\r<BR>\n" );
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document.write( "Another way to calculate it:<BR>\n" );
document.write( "interest = (amount paid back) - (principal)<BR>\n" );
document.write( "interest = (71094) - (22500)<BR>\n" );
document.write( "interest = 48594 dollars<BR>\n" );
document.write( "percent paid interest = (interest/totalPaid)*100%<BR>\n" );
document.write( "percent paid interest = (48594/71094)*100%<BR>\n" );
document.write( "percent paid interest = (0.68352)*100%<BR>\n" );
document.write( "percent paid interest = 68.352%<BR>\n" );
document.write( "and,<BR>\n" );
document.write( "percent paid principal = 100% - (percent paid interest)<BR>\n" );
document.write( "percent paid principal = 100% - (68.352%)<BR>\n" );
document.write( "percent paid principal = 31.648%\r<BR>\n" );
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document.write( "Answers:\r<BR>\n" );
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document.write( "(A) Monthly payment = $236.98<BR>\n" );
document.write( "(B) Total amount paid = $71,094<BR>\n" );
document.write( "(C) 31.648% toward principal, 68.352% to interest<BR>\n" );
document.write( "The decimal values in part (C) are approximate.<BR>\n" );
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document.write( " </SPAN>\n" );
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