document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185341>Question 1185341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bob invests 5000 euros in a fixed deposit that pays a nominal annual interest rate of 4.5% compounded monthly, for seven years. \r<BR>\n" );
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document.write( "Carla has 7000 dollars to invest in a fixed deposit which is compounded annually. She aims to double her money after 10 years. Find the minimum annual interest rate needed for Carla to achieve her aim. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816155 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=816155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'm not actually sure what bob has to do with this.\r<BR>\n" );
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document.write( "i'll handle carla first and then go back to bob if i can figure out what you're asking for there.\r<BR>\n" );
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document.write( "for carla, the formula to use 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 your problem.\r<BR>\n" );
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document.write( "pv = 7000<BR>\n" );
document.write( "fv = 14000<BR>\n" );
document.write( "n = 10 years\r<BR>\n" );
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document.write( "formula becomes 14000 = 7000 * (1 + r) ^ 10\r<BR>\n" );
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document.write( "divide both sides of this equation by 7000 to get:\r<BR>\n" );
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document.write( "2 = (1 + r) ^ 10\r<BR>\n" );
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document.write( "take the 10th root of each side of the eqution to gt:\r<BR>\n" );
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document.write( "2 ^ (1/10) = 1 + r\r<BR>\n" );
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document.write( "subtract 1 from both sides of the equation to get:\r<BR>\n" );
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document.write( "2 ^ (1/10) - 1 = r\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "r = 2 ^ (1/10) - 1 = .0717734625 = 7.17734625%.\r<BR>\n" );
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document.write( "that's the annual interest rate required to double her money in 10 years.\r<BR>\n" );
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document.write( "confirm by replacing r in the original equation and solving for f.\r<BR>\n" );
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document.write( "the equation becomes f = 7000 * (1 + .0717734625) ^ 10.\r<BR>\n" );
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document.write( "solve for f to get:\r<BR>\n" );
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document.write( "f = 14000.\r<BR>\n" );
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document.write( "the solution is that here interest rate per year, compounded annually, need to be at least .0717734625 for her to at least double her money in 10 years.\r<BR>\n" );
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document.write( "back to bob.\r<BR>\n" );
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document.write( "the problem statement is:\r<BR>\n" );
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document.write( "Bob invests 5000 euros in a fixed deposit that pays a nominal annual interest rate of 4.5% compounded monthly, for seven years.\r<BR>\n" );
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document.write( "you probably want to know how much money will be in the account after 7 years.\r<BR>\n" );
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document.write( "the same formula can be used.\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( "the interest rate is 4.5% per year.<BR>\n" );
document.write( "divide that by 12 to get the monthly interest rate of 4.5 / 12 = .375% per month.\r<BR>\n" );
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document.write( ".375% per month is equal to .00375 per month.\r<BR>\n" );
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document.write( "the number of year = 7 * 12 = 84 months.\r<BR>\n" );
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document.write( "the formula becomes f = 5000 * (1 + .00375) ^ 84 = 6847.261285.\r<BR>\n" );
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document.write( "that's the value at the end of the 7 years.\r<BR>\n" );
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document.write( "if you used an online calculator, you would have done the following:\r<BR>\n" );
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document.write( "inputs for carla problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/093002.jpg\" >\r<BR>\n" );
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document.write( "output for carla problem.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/093003.jpg\" >\r<BR>\n" );
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document.write( "inputs for ted problem.\r<BR>\n" );
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document.write( "output for ted problem.\r<BR>\n" );
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document.write( "keep in mind that the formula uses the rate, not the percent and the calculator used the percent, not the rate.\r<BR>\n" );
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document.write( "rate = percent divided by 100.<BR>\n" );
document.write( "percent = rate multiplied by 100.\r<BR>\n" );
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document.write( "in the formula, the interest rate per year is 4.5/100 = .045<BR>\n" );
document.write( "the interest rate per month is .045/12 = .00375\r<BR>\n" );
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document.write( "in the calculator, the interest rate per month is 4.5%/12 = .375%.\r<BR>\n" );
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document.write( "that's for the ted problem.\r<BR>\n" );
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document.write( "for the carla problem, the interest per year from the formula is .0717734625 which you multiply by 100 to get 7.17734625%.\r<BR>\n" );
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document.write( "in the calculator, the interest rate is shown as 7.177346%.\r<BR>\n" );
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document.write( "the difference between the two has to do with carrying out the result to a different number of decimal digits.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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