document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089804>Question 1089804</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your Bank account pays $12,50 as interest at a nominal rate 6%/yearly. What was the balanc of your account 5 months ago? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704186 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=704186\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the interest is 12.50<BR>\n" );
document.write( "the nominal rate if 6% per year.\r<BR>\n" );
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document.write( "if this is simple interest, the formula is i = p * r * n\r<BR>\n" );
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document.write( "i is the interest.<BR>\n" );
document.write( "p is the principal.<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( "the interest rate per time period is the interest rate per year divided by the number of compounding periods per year.\r<BR>\n" );
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document.write( "with simple interest, this doesn't really matter since the interest doesn't compound, so whether you find the interest rate per time period or just use the annual interest rate should give you the same answer.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "the number of compounding periods is months.<BR>\n" );
document.write( "the interest rate per year is 6% which is equal to .06.<BR>\n" );
document.write( "the number of time periods is 5.\r<BR>\n" );
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document.write( "the interest is 12.5.\r<BR>\n" );
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document.write( "the formula becomes 12.5 = p * .06/12 * 6\r<BR>\n" );
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document.write( "divide both sides of this equation by (.06/12 * 5) to get:\r<BR>\n" );
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document.write( "12.5 / (.06/12 * 5) = p\r<BR>\n" );
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document.write( "solve for p to  get p = 12.5 / (.06/12 * 5) = 500\r<BR>\n" );
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document.write( "if you had kept the interest rate per year and made n equal to 6/12, then the formula would have been:\r<BR>\n" );
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document.write( "12.5 = p * .06 * 5/12\r<BR>\n" );
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document.write( "solve for p to get p = 12.5 / (.06 * 5/12) = 500 which is the same.\r<BR>\n" );
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document.write( "when interest is compounded, then the number of compounding periods per year does make a difference, the difference being much more profound when the number of years is larger.  <BR>\n" );
document.write( "for 6 months, the difference is expected to be smaller, but it's still there.\r<BR>\n" );
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document.write( "the formula for compound interest is 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 the number of time periods.\r<BR>\n" );
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document.write( "in this particular case, f is the present value plus the interest which makes f equal to p + 12.5\r<BR>\n" );
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document.write( "the formula becomes p + 12.5 = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "the interest rate per time period is .06 if the number of compounding periods is 1 per year and n becomes 5/12\r<BR>\n" );
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document.write( "the interest rate per time period is .06/12 if the number of compounding periods is 12 per year and n becomes 5.\r<BR>\n" );
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document.write( "assuming time periods of months, the formula becomes:\r<BR>\n" );
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document.write( "p + 12.5 = p * (1 + .06/12) ^ 5\r<BR>\n" );
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document.write( "simplify to get p + 12.5 = p * 1.025251253\r<BR>\n" );
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document.write( "divide both sides of the equation by p to get:\r<BR>\n" );
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document.write( "(p + 12.5) / p = 1.025251253\r<BR>\n" );
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document.write( "simplify to get 1 + 12.5 / p = 1.025251253\r<BR>\n" );
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document.write( "subtract 1 from both sides of the equation to get 12.5 / p = .025251253\r<BR>\n" );
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document.write( "solve for p to get p = 12.5 / .025251253 = 495.0249374\r<BR>\n" );
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document.write( "assuming time periods of years, the formula becomes:\r<BR>\n" );
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document.write( "p + 12.5 = p * (1 + .06) ^ (5/12)\r<BR>\n" );
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document.write( "simplify to get p + 12.5 = p * 1.024575839\r<BR>\n" );
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document.write( "right off the bat, you can see that the factor is different, which will lead to a different present value.\r<BR>\n" );
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document.write( "divide both sides of this equation by p to get (p + 12.5) / p = 1.024575839\r<BR>\n" );
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document.write( "simplify to get 1 + 12.5 / p = 1.024575839\r<BR>\n" );
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document.write( "subtract 1 from both sides to get 12.5 / p = .024575839\r<BR>\n" );
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document.write( "solve for p to get p = 12.5 / .024575839 = 508.629626\r<BR>\n" );
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document.write( "you have 3 possible solutions.\r<BR>\n" );
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document.write( "with simple interest and time periods equal to months, the balance of the account 5 months ago was equal to 500.\r<BR>\n" );
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document.write( "with simple interest and time periods equal to years, the balance of the account 5 months ago was equal to 500.\r<BR>\n" );
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document.write( "with compound interest and time periods equal to months, the balance of the account 5 months ago was equal to 495.0249374\r<BR>\n" );
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document.write( "with compound interest and time periods equal to years, the balance of the account 5 months ago was equal to 508.629626\r<BR>\n" );
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document.write( "so take your pick.\r<BR>\n" );
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document.write( "with simple interest, the balance in the account 5 months ago was 500 and the interest earned is 500 * .06 * 5/12 = 12.5\r<BR>\n" );
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document.write( "with interest compounded monthly, the balance in the account 5 months ago was 495.0249374 and the interest earned is 495.0249374 * (1 + .06/12) ^ 5 - 495.0249374 = 12.5\r<BR>\n" );
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document.write( "with interest compounded annually, the balance in the account 5 months ago was 508.629626 and the interest earned is 508.629626 * (1 + .06) ^ (5/12) - 508.629626 = 12.5\r<BR>\n" );
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document.write( "to calculate interest with simple interest, the formula is straight forward.\r<BR>\n" );
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document.write( "it is i = p * r * n\r<BR>\n" );
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document.write( "i is the interest<BR>\n" );
document.write( "p is the principal<BR>\n" );
document.write( "r is the interest rate per timed period<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "to calculate interest with compound interest, the formula is not quite so straight forward.\r<BR>\n" );
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document.write( "you have to calculate the future value first and then subtract the present value from that to find the interest.\r<BR>\n" );
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document.write( "the formula for compound interest 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 the number of time periods.\r<BR>\n" );
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document.write( "i = f - p\r<BR>\n" );
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document.write( "i is the interest<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value\r<BR>\n" );
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document.write( "the number of compounding periods per year is an important part of the compound interest formula.\r<BR>\n" );
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document.write( "the interest rate per time period is the annual interest rate divided by the number of compounding periods per year and the number of time periods is the number of years times the number of compounding periods per year.\r<BR>\n" );
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document.write( "any questions regarding this, give me a shout.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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