document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131695>Question 1131695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Carissa's parents were unable to pay for her last year of college, so she obtained a student loan of $9,000. The conditions of the loan were: She would make no payments while in college, but the interest would accumulate at 3.0% compounded monthly. Upon graduation she would begin equal monthly payments that would repay the loan in 4 years. (Round your answers to the nearest cent.)<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 #748358 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=748358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i used the following online calculator to assist me in solving this.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "the loan is for $9,000.<BR>\n" );
document.write( "no payments are made while in college.<BR>\n" );
document.write( "interest will be 3% compounded monthly.\r<BR>\n" );
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document.write( "the loan is for the last year in college.\r<BR>\n" );
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document.write( "the formula to find the future value of the loan after 1 year is:\r<BR>\n" );
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document.write( "f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the interest rate per time period<BR>\n" );
document.write( "n is then number of time periods.\r<BR>\n" );
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document.write( "the time periods are months.\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "f is what you want to find.<BR>\n" );
document.write( "p is 9,000<BR>\n" );
document.write( "r = 3% / 100 = .03 / 12 = .0025<BR>\n" );
document.write( "n = 1 * 12 = 12\r<BR>\n" );
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document.write( "the formula becomes f = 9000 * (1 + .0025) ^ 12.\r<BR>\n" );
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document.write( "the result is f = 9273.743612\r<BR>\n" );
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document.write( "that future value becomes the present value of the loan.\r<BR>\n" );
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document.write( "the use of a financial calculator is recommended here, even though there is a formula that can be used as well.\r<BR>\n" );
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document.write( "financial formulas can be found at <a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#notes\" target = \"_blank\">https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#notes</a>\r<BR>\n" );
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document.write( "the particular formula used here would be:\r<BR>\n" );
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document.write( "ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS \r<BR>\n" );
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document.write( "a = (p*r)/(1-(1/(1+r)^n)) \r<BR>\n" );
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document.write( "a is the annuity.<BR>\n" );
document.write( "p is the present amount.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods. \r<BR>\n" );
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document.write( "i used the calculator, but the formula should provide you with the same answer.\r<BR>\n" );
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document.write( "the main difference between the use of either is that the formula uses the interest rate while the calculator uses the interest rate percent.\r<BR>\n" );
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document.write( "rate = rate percent / 100.<BR>\n" );
document.write( "rate percent = rate * 100.\r<BR>\n" );
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document.write( "the inputs to the calculator would be:\r<BR>\n" );
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document.write( "present value = 9273.743612<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "number of time periods = 12 * 4 = 48<BR>\n" );
document.write( "interest rate percent per time period = 3/12 = .25<BR>\n" );
document.write( "payments are made at the end of each time period.\r<BR>\n" );
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document.write( "click on PMT and you get the payments required at the end of each month.\r<BR>\n" );
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document.write( "the calculator tells you that the payment required is 205.27 at the end of each month.\r<BR>\n" );
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document.write( "the payment is shown as negative because it is money going out, while the present value is shown as positive because it is money that has already come in.\r<BR>\n" );
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document.write( "at the end of the 48 months, the remaining balance of money owed is equal to 0 and the loan is paid off.\r<BR>\n" );
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document.write( "here's what the results of the calculator look like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/121401.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "in the formula above, a is the annuity which is the same as the monthly payment.\r<BR>\n" );
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document.write( "if you try to use the formula, your inputs would be:\r<BR>\n" );
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document.write( "p = 9273.73612<BR>\n" );
document.write( "r = .03/12 = .0025<BR>\n" );
document.write( "n = 4 * 12 = 48\r<BR>\n" );
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document.write( "the formula of a = (p*r)/(1-(1/(1+r)^n)) becomes:\r<BR>\n" );
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document.write( "a = (9273.73612 * .0025) / (1 - (1 / (1 + .0025) ^ 48 )).\r<BR>\n" );
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document.write( "the result is a = 205.2680735 which is rounded to 205.27.\r<BR>\n" );
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document.write( "when you use the formula, be sure to make your entries into your calculator exactly as shown since any deviation could result in a wrong answer.\r<BR>\n" );
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document.write( "use of the calculator is just so much easier.\r<BR>\n" );
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document.write( "if you want to know the total interest that was paid, you would multiply the loan payments * 48 and then subtract the principal of the loan.\r<BR>\n" );
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document.write( "that would be 205.2680735 * 48 - 9273.73612 = 579.1239171 rounded to 579.12.\r<BR>\n" );
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document.write( "the general concepts used here are:\r<BR>\n" );
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document.write( "the present value of the loan repayment is the future value of the loan after 1 year.<BR>\n" );
document.write( "the total interest paid is the payment at the end of each month times the number of months minus the present value of the loan repayment.\r<BR>\n" );
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document.write( "for what you needed to do, the solution is:\r<BR>\n" );
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document.write( "not exactly sure, but i suspect the value of the monthly payment, which is 205.27 payable at the end of each month for a period of 48 months.\r<BR>\n" );
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document.write( "the interest rate on the loan is assumed to be the same throughout the loan period, which includes the 1 year of no payments plus 4 years of payments.\r<BR>\n" );
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