document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=849282>Question 849282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> BofA offer two programs for a car loan, 1st program offer is based on simple interest of 6.8% for four years. The 2nd program is based on a compound monthly with interest rate of 5.5% for four years. Joan is considering to borrow $12,500 to buy a car and ask your opinion for the loan. Which loan would you suggest to her and why. How much interest she will pay on both loans after 32 months? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511483 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=511483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simple Interest Loan:\r<BR>\n" );
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document.write( "I = P * R * T\r<BR>\n" );
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document.write( "I = interest<BR>\n" );
document.write( "P = principal<BR>\n" );
document.write( "R = Interest Rate per Time Period<BR>\n" );
document.write( "T = Number of Time Periods\r<BR>\n" );
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document.write( "In your problem:\r<BR>\n" );
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document.write( "P = 12,500<BR>\n" );
document.write( "R = .068 per year.<BR>\n" );
document.write( "T = 4 years<BR>\n" );
document.write( "I = Interest\r<BR>\n" );
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document.write( "Replace P with 12,500 and R with .068 and T with 4 and the simple interest formula becomes:\r<BR>\n" );
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document.write( "I = 12,500 * .068 * 4 = $3,400.\r<BR>\n" );
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document.write( "Compound Interest Loan:\r<BR>\n" );
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document.write( "F = P * (1+R)^T<BR>\n" );
document.write( "I = F - P\r<BR>\n" );
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document.write( "Combine these formulas together and you get:\r<BR>\n" );
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document.write( "I = P * (1+R)^T - P\r<BR>\n" );
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document.write( "Simplify this formula further using the distributive law and you get:\r<BR>\n" );
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document.write( "I = P * ((1+R)^T - 1)\r<BR>\n" );
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document.write( "You can use the formula in either form to get your answer.\r<BR>\n" );
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document.write( "The forms are:\r<BR>\n" );
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document.write( "F = P * (1+R)^T<BR>\n" );
document.write( "I = F - P\r<BR>\n" );
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document.write( "I = P * (1+R)^T - P\r<BR>\n" );
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document.write( "I = P * ((1+R)^T - 1)\r<BR>\n" );
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document.write( "I used the first form which calculates the future value of the loan first and then calculates the interest by subtracting the principal.\r<BR>\n" );
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document.write( "F = Future Value of the loan which is the amount you have to pay back at maturity.<BR>\n" );
document.write( "P = Principal or what is also known as the Present Value of the loan.<BR>\n" );
document.write( "R = Interest Rate per Time Period<BR>\n" );
document.write( "T = Number of Time Periods.<BR>\n" );
document.write( "I = Interest\r<BR>\n" );
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document.write( "In your problem:\r<BR>\n" );
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document.write( "P = 12,500<BR>\n" );
document.write( "R = .055 per year divided by 12 months = .00458333 per month.<BR>\n" );
document.write( "T = 4 years * 12 compounding periods per year = 48 months.\r<BR>\n" );
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document.write( "Replace P with 12,500 and R with .00458333 and T with 48 and the compound interest formula becomes:\r<BR>\n" );
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document.write( "F = 12,500 * (1.0094583)^48 = $15,568.\r<BR>\n" );
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document.write( "Replace F with 15,568 and the I = F - P formula becomes:\r<BR>\n" );
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document.write( "I = 15,568 - 12,500 = $3,068.\r<BR>\n" );
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document.write( "She should take the second loan because she will pay over $300.00 less in interest over the 4 year period.\r<BR>\n" );
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document.write( "After 32 months, the interest on the simple interest loan will be equal to:\r<BR>\n" );
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document.write( "I = P * R * T = 12,500 * l068 * (32/12) = $2,266.67\r<BR>\n" );
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document.write( "Since T is in years, you need to divide 32 by 12 to get the equivalent number of years.\r<BR>\n" );
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document.write( "After 32 months, the interest on the compound interest loan will be equal to:\r<BR>\n" );
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document.write( "F = P * (1 + R) ^ T = 12,500 * (1.004583333) ^ 32 = 14,469.75 - 12,500 = $1,969.75\r<BR>\n" );
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document.write( "With simple interest, you can calculate the interest directly.<BR>\n" );
document.write( "With compound interest, you have to calculate the future value of the loan and then subtract the principal from that to get the interest.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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