document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150114>Question 1150114</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A high school student would like to save $50,000 for her year end party.<BR>\n" );
document.write( "How much should she deposit in a savings account every week for 15 weeks if the interest is at 0.25%<BR>\n" );
document.write( "compounded monthly?\r<BR>\n" );
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document.write( "I am confused at what $50,000 represents. Is it the Principal value, future value, or the interest? Thank you.<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 #771479 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=771479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'll solve the problem and then explain what i did as best i can.\r<BR>\n" );
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document.write( "i used the TI-BA-II financial calculator.<BR>\n" );
document.write( "the BA stands for Business Analyst.\r<BR>\n" );
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document.write( "my entries are:<BR>\n" );
document.write( "pv = 0<BR>\n" );
document.write( "fv = 50,000 (entered without the comma)<BR>\n" );
document.write( "r = .0048073071%<BR>\n" );
document.write( "n = 15\r<BR>\n" );
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document.write( "the calculator tells me that the weekly payments need to be 3332.211772.\r<BR>\n" );
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document.write( "the total payments = 15 * that = 49,983.17658.\r<BR>\n" );
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document.write( "the rest is interest earned from the weekly payments of 3332.211772.\r<BR>\n" );
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document.write( "i used excel to show the remaining weekly balance.\r<BR>\n" );
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document.write( "it is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/120804.jpg\" alt = \"$$$\" >\r<BR>\n" );
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document.write( "i also used an online calculator at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/index.html\" target = \"_blank\">https://arachnoid.com/finance/index.html</a> to show you what the inputs would look like and what the output would look like if you used this online calculator.\r<BR>\n" );
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document.write( "the inputs to this calculator are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/120805.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the output from this calculator is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/120806.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "one answer to your question.\r<BR>\n" );
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document.write( "the principal is the amount that is invested.<BR>\n" );
document.write( "in your problem, that would be the $3,332.21 that is invested at the end of each week for 15 weeks.<BR>\n" );
document.write( "the future value is the principal plus interest earned during the 15 week investment period.<BR>\n" );
document.write( "your total investment was 15 * 3,332.21 = $49,983.15<BR>\n" );
document.write( "the difference between that and the future value was the interest, which equaled $16.85.\r<BR>\n" );
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document.write( "the calculation of the weekly interest rate was critical to the success of this procedure.\r<BR>\n" );
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document.write( "the yearly interest rate percent was divided by 12 to get the monthly interest rate percent.\r<BR>\n" );
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document.write( "this was divided by 100 to get the monthly interest rate.\r<BR>\n" );
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document.write( "1 was added to this and the result was then raised to the 12/52 power to get the weekly interest rate plus 1.\r<BR>\n" );
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document.write( "1 was subtracted from this to get the weekly interest rate.\r<BR>\n" );
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document.write( "this was multiplied by 100 to get the weekly interest rate percent.\r<BR>\n" );
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document.write( "the weekly interest rate percent is what was entered as the rate in the calculator.\r<BR>\n" );
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document.write( "this was calculated to be ((1 + .25/1200) ^ (12/52) - 1) * 100 = .0048073071.\r<BR>\n" );
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document.write( "note that .25/1200 is equal to .25 / 12 to get the monthly interest rate percent which is divided by 100  to get the monthly interest rate.\r<BR>\n" );
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document.write( "note that when you raise that to the (12/52) power, you are raising it to the 12th power to get the effect yearly interest rate + 1, and then you are taking the 52d root of that to get the weekly interest rate + 1.\r<BR>\n" );
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document.write( "the procedure to find the weekly interest rate percent is shown below.\r<BR>\n" );
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document.write( ".25% is the yearly interest rate percent which is also known as the apr (annual percentage rate).<BR>\n" );
document.write( ".25% / 100 = .0025 is the yearly interest rate.<BR>\n" );
document.write( "this is divided by 12 to get the monthly rate.<BR>\n" );
document.write( ".0025 / 12 = .0002083333333 = the monthly interest rate.<BR>\n" );
document.write( "add 1 to this to get 1.00020833333.<BR>\n" );
document.write( "raise  that to the 12th power to get the effective yearly interest rate plus 1.<BR>\n" );
document.write( "subtract 1 from that to get the effective yearly interest rate.<BR>\n" );
document.write( "multiply that by 100 to get the effective yearly interest rate percent.<BR>\n" );
document.write( "effective yearly interest rate + 1 = (1.00020833333) ^ 12 = 1.002502867<BR>\n" );
document.write( "1.002502867 - 1 = .002502867 = the effective yearly interest rate.<BR>\n" );
document.write( ".002502867 * 100 = .2502867 = the effective yearly interest rate percent.<BR>\n" );
document.write( "take the 52d root of the effective yearly interest rate + 1 to get the weekly interest rate + 1.<BR>\n" );
document.write( "that is equal to (1.002502867) ^ (1/52) = 1.000048073.<BR>\n" );
document.write( "subtract 1 from that to get the weekly interest rate.<BR>\n" );
document.write( "that is equal to  .000048073071<BR>\n" );
document.write( "multiply that by 100 to get the weekly interest rate percent.<BR>\n" );
document.write( "that is equal to .0048073071.<BR>\n" );
document.write( "that is what was entered into the calculator as the weekly interest rate percent.\r<BR>\n" );
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document.write( "the number of time periods in the calculator was set to 15 because you were investing at the end of each week for 15 weeks.\r<BR>\n" );
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document.write( "the last input is telling you that the investment is made at the end of each week.<BR>\n" );
document.write( "that's the switch where you select beginning or end.\r<BR>\n" );
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document.write( "the only nominal interest rate was the yearly interest rate.<BR>\n" );
document.write( "that was divided by 12 to get the monthly interest rate.<BR>\n" );
document.write( "the monthly interest rate and the weekly interest rate were both effective interest rates.\r<BR>\n" );
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document.write( "this is a lot to understand.<BR>\n" );
document.write( "if you need to ask any further questions about it, send me an email and i'll answer as best i can.\r<BR>\n" );
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document.write( "your solution is that she has to deposit $3,332.21 at the end of each week for 15 weeks so that she will have $50,000 for her year end party. </SPAN>\n" );
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