document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248887>Question 248887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I cannot get this answer correct to save my life. Could someone please help me. Thank you very much.\r<BR>\n" );
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document.write( "On September 8, Bert Sarkis joined a Christmas club. His bank will automatically deduct $65 from his checking account at the end of each month and deposit it into his Christmas club account, where it will earn 6% interest. The account comes to term on December 1. \r<BR>\n" );
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document.write( "(a) Find the future value of the account, using an annuity formula. (Round your answer to the nearest cent.)\r<BR>\n" );
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document.write( "(b) Find the future value of the account, using the compound interest formula. (Round your answer to the nearest cent.)\r<BR>\n" );
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document.write( "(c) Find Bert's total contribution to the account.\r<BR>\n" );
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document.write( "(d) Find the total interest. (Round your answer 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 #181364 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=181364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> bert joined the christmas club on september 8th.<BR>\n" );
document.write( "65 dollars is deducted from his checking account at the end of every month and deposited into the christmas club account.<BR>\n" );
document.write( "the christmas club account earns 6% interest a year.<BR>\n" );
document.write( "the account comes to term on december 1.\r<BR>\n" );
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document.write( "here's how it works.\r<BR>\n" );
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document.write( "the annual interest rate is 6%.<BR>\n" );
document.write( "the monthly rate is 6% / 12% = .5% / 100% = .005\r<BR>\n" );
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document.write( "the account starts at 0.<BR>\n" );
document.write( "at the end of september the account has 65 dollars in it.<BR>\n" );
document.write( "at the end of october the account has 65 * 1.005 + 65 = 130.325 dollars in it.<BR>\n" );
document.write( "at the end of november the account has 130.325 * 1.005 + 65 = 195.976625 dollars in it.<BR>\n" );
document.write( "on december 1st, the account has $195.98 in it.\r<BR>\n" );
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document.write( "your questions are:\r<BR>\n" );
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document.write( "(a) Find the future value of the account, using an annuity formula. (Round your answer to the nearest cent.)\r<BR>\n" );
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document.write( "See the bottom for how to solve this using the annuity formula.\r<BR>\n" );
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document.write( "(b) Find the future value of the account, using the compound interest formula. (Round your answer to the nearest cent.)\r<BR>\n" );
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document.write( "This was done up top when I provided you with the month by month details.\r<BR>\n" );
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document.write( "(c) Find Bert's total contribution to the account.\r<BR>\n" );
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document.write( "Bert's total contribution was 3 * 65 = $195.00\r<BR>\n" );
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document.write( "(d) Find the total interest. (Round your answer to the nearest cent.)\r<BR>\n" );
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document.write( "The total interest was $.98\r<BR>\n" );
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document.write( "the assumption is that the interest is an annual interest rate.\r<BR>\n" );
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document.write( "to convert that to monthly interest rate you have to divide it by 12.\r<BR>\n" );
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document.write( "SOLVING USING AN ANNUITY FORMULA\r<BR>\n" );
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document.write( "The formula you want is future value of a payment.\r<BR>\n" );
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document.write( "payments and annuities are terms that are sometimes used interchangeably.\r<BR>\n" );
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document.write( "future value of a payment formula is the same as future value of an annuity formula.\r<BR>\n" );
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document.write( "sometimes they call it future worth rather than future value.\r<BR>\n" );
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document.write( "that formula is:\r<BR>\n" );
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document.write( "FUTURE VALUE OF A PAYMENT\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+FV%28PMT%29+=+%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29+ ALIGN=MIDDLE  ALT=\"+FV%28PMT%29+=+%28PMT+%2A+%28%281%2Bi%29%5En-1%29%2Fi%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "FV = future value<BR>\n" );
document.write( "PMT = payment per time period<BR>\n" );
document.write( "i = interest rate per time period<BR>\n" );
document.write( "n = 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( "FV = x<BR>\n" );
document.write( "PMT = 65<BR>\n" );
document.write( "i = .06 / 12 = .005<BR>\n" );
document.write( "n = 3 (you make payments in september, october, and november)\r<BR>\n" );
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document.write( "this formula assumed end of time period payments.\r<BR>\n" );
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document.write( "your formula becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%2865+%2A+%28%281.005%29%5E3-1%29%2F.005%29+ ALIGN=MIDDLE  ALT=\"+x+=+%2865+%2A+%28%281.005%29%5E3-1%29%2F.005%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "your answer becomes:\r<BR>\n" );
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document.write( "x = 195.976625\r<BR>\n" );
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document.write( "this round out to x = $195.98\r<BR>\n" );
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document.write( "I confirmed using a financial calculator.\r<BR>\n" );
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document.write( "the principal is number of payments times the payment = 3 * 65 = 195.\r<BR>\n" );
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document.write( "the interest is the future value of the payments minus the payments = 195.98 minus 195 = .98\r<BR>\n" );
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