document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194151>Question 1194151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> MAT: Topics in Contemporary Math\r<BR>\n" );
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document.write( " Loans\r<BR>\n" );
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document.write( "3) Adventuresome Alex REALLY wants to buy an RV and live out in the wilderness, away <BR>\n" );
document.write( "from the hassles of city living. They decide they can afford a monthly payment of $415 <BR>\n" );
document.write( "and their lending agency offers a 3.0% annual interest rate on a 10-year loan.<BR>\n" );
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document.write( "a. What is the total value of the loan? \r<BR>\n" );
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document.write( "b. What was the total amount Adventuresome Alex paid their lending agency? \r<BR>\n" );
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document.write( "c. How much did they pay in interest? <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 #826274 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=826274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The monthly payment formula is<BR>\n" );
document.write( "P = (L*i)/( 1-(1+i)^(-n) )<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "P = monthly payment<BR>\n" );
document.write( "L = loan amount<BR>\n" );
document.write( "i = interest rate per month, in decimal form<BR>\n" );
document.write( "n = number of months\r<BR>\n" );
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document.write( "In this case we have,<BR>\n" );
document.write( "P = 415<BR>\n" );
document.write( "L = unknown and what we want to solve for<BR>\n" );
document.write( "i = 0.03/12 = 0.0025 exactly<BR>\n" );
document.write( "n = 12*10 = 120 months (equivalent to 10 years)\r<BR>\n" );
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document.write( "Let's plug those known values in, and solve for L<BR>\n" );
document.write( "P = (L*i)/( 1-(1+i)^(-n) )<BR>\n" );
document.write( "415 = (L*0.0025)/( 1-(1+0.0025)^(-120) )<BR>\n" );
document.write( "415 = L * [ (0.0025)/( 1-(1+0.0025)^(-120) ) ]<BR>\n" );
document.write( "415 = L * 0.00965607446983<BR>\n" );
document.write( "L = 415/0.00965607446983<BR>\n" );
document.write( "L = 42,978.1275296343<BR>\n" );
document.write( "L = 42,978.13<BR>\n" );
document.write( "which is the total value of the loan if Alex paid the max monthly payment of $415<BR>\n" );
document.write( "That wraps up part (a)\r<BR>\n" );
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document.write( "For part (b), we multiply the $415 monthly payment by the 120 months to figure out how much Alex pays back (principal + interest)<BR>\n" );
document.write( "415*120 = 49,800 dollars is the answer to part (b)\r<BR>\n" );
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document.write( "In part (c), we subtract the results of part (b) and part (a) in that order<BR>\n" );
document.write( "49,800 - 42,978.13 = 6,821.87<BR>\n" );
document.write( "That's the amount of total interest paid\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "(a) $42,978.13<BR>\n" );
document.write( "(b) $49,800<BR>\n" );
document.write( "(c) $6,821.87<BR>\n" );
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