document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098670>Question 1098670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a loan is repaid with equal payments of 200 dollar at the end of each week for 15 years .if interest is 10.4% p.a. compounded weekly and assuming that there are 52 weeks in a year,<BR>\n" );
document.write( "(a)  the total amount repaid,<BR>\n" );
document.write( "(b)  the present value of the loan (correct to 2 decimal places),<BR>\n" );
document.write( "(c)  the total amount of interest paid (correct to 2 decimal places).\r<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 #713058 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=713058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> payments are 200 dollars at the end of each week for 15 years.<BR>\n" );
document.write( "interest rate is 10.4% per year compounded weekly.<BR>\n" );
document.write( "assuming 52 weeks in a year, you would translate this problem as follows for the online calculator at \r<BR>\n" );
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document.write( "present value = 0<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "number of periods = 15 * 52 = 780 weeks<BR>\n" );
document.write( "payment amount = -200<BR>\n" );
document.write( "interest rate % per period = 10.4 / 52 = .2<BR>\n" );
document.write( "payment made at end of time period\r<BR>\n" );
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document.write( "you would then click on PV and the calculator will tell you that the present value of the loan is $78,953.63\r<BR>\n" );
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document.write( "the total payments you made would be 780 * $200 = $156,000\r<BR>\n" );
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document.write( "the total interest you paid would be $156,000 - $78,953.63 = $77,046.37\r<BR>\n" );
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document.write( "the calculator i used is at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "here's a picture of the results from this calculator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/102310.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "you could also have calculated manually using the following formula.\r<BR>\n" );
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document.write( "PRESENT VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS \r<BR>\n" );
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document.write( "p = (a*(1-1/(1+r)^n))/r \r<BR>\n" );
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document.write( "p is the present value of the annuity.<BR>\n" );
document.write( "a is the annuity.<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( "in your problem:\r<BR>\n" );
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document.write( "a = 200<BR>\n" );
document.write( "r = 10.4 / 100 = .104 / 52 = .002<BR>\n" );
document.write( "n = 15 * 52 = 780\r<BR>\n" );
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document.write( "the formula of p = (a*(1-1/(1+r)^n))/r becomes:\r<BR>\n" );
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document.write( "p = (200*(1-1/(1.002)^780))/.002\r<BR>\n" );
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document.write( "the result would be p = $78,953.62978 which is equal to $78,953.63 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "that's the same result that the calculator gave you.\r<BR>\n" );
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document.write( "a summary of financial formulas that you might find useful can be found at this link.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f5\" target = \"_blank\">https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f5</a><BR>\n" );
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