document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199059>Question 1199059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I am having trouble with using a TVM solver. I am not sure if I'm getting the right answers. I'd love it if someone could help me. The question is:\r<BR>\n" );
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document.write( "Use a TVM Solver:<BR>\n" );
document.write( "A) $2,500.00 investment earns interest at 7.5% compounded monthly. How long will it take it to double?\r<BR>\n" );
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document.write( "B) At what interest rate should $1,500.00 be invested, if you want to have $2,000.00 in 10 years compounded daily?\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 #832761 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832761\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "If you have a TI83 or TI84, then follow the steps mentioned below. <BR>\n" );
document.write( "If not, then skip to the next section.\r<BR>\n" );
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document.write( "Press the button labeled \"APPS\". <BR>\n" );
document.write( "It is likely a different color from the rest of the buttons.\r<BR>\n" );
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document.write( "Go to \"Finance\", then \"TVM Solver\"\r<BR>\n" );
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document.write( "Check out this page for a few examples<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://people.tamu.edu/~kahlig//calc/tvm-solver.html\">https://people.tamu.edu/~kahlig//calc/tvm-solver.html</a>\r<BR>\n" );
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document.write( "For part (a), type the following values<BR>\n" );
document.write( "N = 0<BR>\n" );
document.write( "I = 7.5<BR>\n" );
document.write( "PV = -2500<BR>\n" );
document.write( "PMT = 0<BR>\n" );
document.write( "FV = 5000<BR>\n" );
document.write( "P/Y = 1<BR>\n" );
document.write( "C/Y = 12\r<BR>\n" );
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document.write( "N = number of periods = number of years in this case<BR>\n" );
document.write( "I = interest rate in percent form<BR>\n" );
document.write( "PV = present value<BR>\n" );
document.write( "PMT = payment per period<BR>\n" );
document.write( "FV = future value<BR>\n" );
document.write( "P/Y = the number of payments per year<BR>\n" );
document.write( "C/Y = the number of compounding periods per year\r<BR>\n" );
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document.write( "The PV is negative because it's a cash outflow. <BR>\n" );
document.write( "Positive values are cash inflows.<BR>\n" );
document.write( "The PMT is 0 because you aren't making periodic deposits; rather you make a one-time deposit.\r<BR>\n" );
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document.write( "After those values are inputted, scroll back up to the first line N = 0<BR>\n" );
document.write( "Then press the green \"alpha\" key and then hit \"enter\"<BR>\n" );
document.write( "This will then solve for N to get roughly 9.270813549\r<BR>\n" );
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document.write( "In other words, the N = 0 will update to N = 9.270813549\r<BR>\n" );
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document.write( "It takes about 9.270813549 years for the money to double at this interest rate, when compounded monthly.\r<BR>\n" );
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document.write( "0.270813549 years = 12*0.270813549 = 3.249762588<BR>\n" );
document.write( "telling us that<BR>\n" );
document.write( "9.270813549 years = 9 years + 3.249762588 months\r<BR>\n" );
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document.write( "In short, it takes about 9 years + 4 months for the money to double. <BR>\n" );
document.write( "I rounded up to the nearest whole month to guarantee the money cleared the doubling threshold.\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "Here's an alternative TVM solver if you don't have a TI83 or TI84 calculator.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.geogebra.org/m/mvv2nus2\">https://www.geogebra.org/m/mvv2nus2</a><BR>\n" );
document.write( "The person who made this did so with the goal of emulating the TI83/TI84 calculator's TVM solver.\r<BR>\n" );
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document.write( "The inputs for that calculator would be the same as mentioned earlier.\r<BR>\n" );
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document.write( "Here's another alternative TVM solver<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://arachnoid.com/finance/\">https://arachnoid.com/finance/</a><BR>\n" );
document.write( "While this solver doesn't allow you to specify compounding frequency, we can make an adjustment on the interest rate.<BR>\n" );
document.write( "Instead of 7.5%, we would have (7.5%)/12 = 0.625% as the monthly interest rate<BR>\n" );
document.write( "That TVM solver will produce N = 111.25 to indicate 111.25 months<BR>\n" );
document.write( "111.25 months = (111.25)/12 = 9.2708 years approximately\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "Let's say we wanted to know what's going on under the hood of these TVM solvers.\r<BR>\n" );
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document.write( "Recall the compound interest formula is<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)\r<BR>\n" );
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document.write( "where,<BR>\n" );
document.write( "A = final value after t years<BR>\n" );
document.write( "P = deposit<BR>\n" );
document.write( "r = interest rate in decimal form<BR>\n" );
document.write( "n = number of times the money is compounded per year<BR>\n" );
document.write( "t = number of years\r<BR>\n" );
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document.write( "In the case of part (a)<BR>\n" );
document.write( "A = 5000 which is double of 2500<BR>\n" );
document.write( "P = 2500<BR>\n" );
document.write( "r = 0.075<BR>\n" );
document.write( "n = 12<BR>\n" );
document.write( "t = unknown\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "5000 = 2500*(1+0.075/12)^(12*t)<BR>\n" );
document.write( "5000/2500 = (1.00625)^(12*t)<BR>\n" );
document.write( "2 = (1.00625)^(12*t)<BR>\n" );
document.write( "log( 2 ) = log(  (1.00625)^(12*t) )<BR>\n" );
document.write( "log( 2 ) = 12*t*Log( 1.00625 )<BR>\n" );
document.write( "t = log(2)/(12*log(1.00625))<BR>\n" );
document.write( "t = 9.270813549\r<BR>\n" );
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document.write( "We get the same answer as earlier to help confirm the answer is correct.\r<BR>\n" );
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document.write( "Everything mentioned so far was for part (a)\r<BR>\n" );
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document.write( "Now onto part (b)\r<BR>\n" );
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document.write( "Go back to your favorite TVM solver of choice to plug in these values:<BR>\n" );
document.write( "N = 10<BR>\n" );
document.write( "I = 0<BR>\n" );
document.write( "PV = -1500<BR>\n" );
document.write( "PMT = 0<BR>\n" );
document.write( "FV = 2000<BR>\n" );
document.write( "P/Y = 1<BR>\n" );
document.write( "C/Y = 365\r<BR>\n" );
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document.write( "The I = 0 will be updated after we use the solver to determine the interest rate. <BR>\n" );
document.write( "For some TVM solvers, you'll leave that entry blank.\r<BR>\n" );
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document.write( "After using the TVM solver, you should get I = 2.88% approximately\r<BR>\n" );
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document.write( "Here's what the steps look like if we were to use the compound interest formula so we can solve for the variable r.\r<BR>\n" );
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document.write( "A = P*(1+r/n)^(n*t)<BR>\n" );
document.write( "2000 = 1500*(1+r/365)^(365*10)<BR>\n" );
document.write( "2000/1500 = (1+r/365)^(3650)<BR>\n" );
document.write( "1.333333333 = (1+r/365)^(3650)<BR>\n" );
document.write( "(1+r/365)^(3650) = 1.333333333<BR>\n" );
document.write( "1+r/365 = (1.333333333)^(1/3650)<BR>\n" );
document.write( "1+r/365 = 1.00007882<BR>\n" );
document.write( "r/365 = 1.00007882 - 1<BR>\n" );
document.write( "r/365 = 0.00007882<BR>\n" );
document.write( "r = 365*0.00007882<BR>\n" );
document.write( "r = 0.0287693\r<BR>\n" );
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document.write( "We get an interest rate of roughly r*100% = 0.0287693*100% = 2.87693% which rounds to 2.88% found earlier.<BR>\n" );
document.write( "This helps confirm the answer.\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "Summary:\r<BR>\n" );
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document.write( "Answer to part (a) is <font color=red>9.27 years</font>, or <font color=red>9 years, 4 months</font> when rounding up to the nearest month.\r<BR>\n" );
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document.write( "Answer to part (b) is <font color=red>2.88%</font>\r<BR>\n" );
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document.write( "Each answer is approximate. <BR>\n" );
document.write( "Round each decimal value according to the instructions your teacher provides; or seek further clarification of rounding instructions.<BR>\n" );
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