document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132297>Question 1132297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John joined the wazalendo saving and credit society and agree to contribute share of Tsh,1600000 at the end of each year from a salary. Find<BR>\n" );
document.write( "(a). The value of this fund at the end of 5 years and.<BR>\n" );
document.write( "(b). The present value of the money after period of installments if money is worth 6% per annum compound interest  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749320 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=749320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the investment is 1.6 million tanzanian shillings at the end of each year for 5 years.\r<BR>\n" );
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document.write( "the interest rate is 6% per year.\r<BR>\n" );
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document.write( "there are several ways to solve this, the easiest being to use a financial calculator.\r<BR>\n" );
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document.write( "there are also formulas that i will give to you.\r<BR>\n" );
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document.write( "lastly, you can solve it the hard way by doing it manually.\r<BR>\n" );
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document.write( "this is not recommended but available when the number of calculations is not overly large.\r<BR>\n" );
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document.write( "first the use of a calculator.\r<BR>\n" );
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document.write( "the online calculator i used can be found at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blaqnk\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "your total investment is 1.6 million at the end of each year for 5 years.\r<BR>\n" );
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document.write( "this is equal to 5 * 1.6 = 8 million = 8,000,000\r<BR>\n" );
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document.write( "the present value is calculated by making the following inputs to the calculator.\r<BR>\n" );
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document.write( "present value = 0<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "payment at the end of each time period = -1600000<BR>\n" );
document.write( "interest rate percent for each time period = 6%.<BR>\n" );
document.write( "number of time periods = 5\r<BR>\n" );
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document.write( "you then click on pv and it tell you that the present value is 6,739,782.06 tanzanian shillings.\r<BR>\n" );
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document.write( "here's what it looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/010501.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the future value is calculated by making the following inputs to the calculator.\r<BR>\n" );
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document.write( "present value = 0<BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "payment at the end of each time period = -1600000<BR>\n" );
document.write( "interest rate percent for each time period = 6%.<BR>\n" );
document.write( "number of time periods = 5\r<BR>\n" );
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document.write( "you then click on fv and it tell you that the present value is 9,019,348.74 tanzanian shillings.\r<BR>\n" );
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document.write( "here's what it looks like.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/010502.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "there is a formula you can use that should give you the same answer.\r<BR>\n" );
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document.write( "that formula can be found in the following reference:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#notes\" target = \"_blank\">https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#notes</a>\r<BR>\n" );
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document.write( "the formula to be used for the present value is:\r<BR>\n" );
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document.write( "PRESENT VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS \r<BR>\n" );
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document.write( "p = (a*(1-1/(1+r)^n))/r \r<BR>\n" );
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document.write( "p is the present value of the annuity.<BR>\n" );
document.write( "a is the annuity.<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 formula to be used for the future value is:\r<BR>\n" );
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document.write( "FUTURE VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS \r<BR>\n" );
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document.write( "f = (a*((1+r)^n-1))/r \r<BR>\n" );
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document.write( "f is the future value of the annuity.<BR>\n" );
document.write( "a is the annuity.<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( "you would enter the appropriate values into your calculator exactly as shown and you should get the same answer that the calculator gave you after rounding to 2 decimal places.\r<BR>\n" );
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document.write( "for the present value, your entries to the calculator will be:\r<BR>\n" );
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document.write( "(1600000*(1-1/(1+.06)^5))/.06\r<BR>\n" );
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document.write( "the calculator will tell you that the present value is equal to 6739782.057 which is rounded to 6739782.06 which is equal to 6,739,782.06 after commas are included.\r<BR>\n" );
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document.write( "this agrees with what the calculator told you.\r<BR>\n" );
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document.write( "for the future value, your entries to the calculator will be:\r<BR>\n" );
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document.write( "(1600000*((1+.06)^5-1))/.06\r<BR>\n" );
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document.write( "the calculator will tell you that the future value is equal to 9019348.736 which is rounded to 9019348.74 which is equal to 9,019,348.74 after commas are included.\r<BR>\n" );
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document.write( "lastly, you can do the calculator manually through the use of your calculator.\r<BR>\n" );
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document.write( "you essentially have 5 investments in each time period.\r<BR>\n" );
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document.write( "your time periods are from time period 0 to time period 5.\r<BR>\n" );
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document.write( "time period 1 is the end of year 1.<BR>\n" );
document.write( "time period 2 is the end of year 2.<BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( "to find the total investment, you add up the investments in each time period.\r<BR>\n" );
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document.write( "to find the present value, you divide each time period investment by 1.06 raised to the power of the time period.\r<BR>\n" );
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document.write( "investment in time period 1 is divided by 1.06.<BR>\n" );
document.write( "investment in time period 2 is divided by 1.06 ^ 2.<BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( "to find the future fvalue, you multiply each time period investment by 1.06 raised to the power of 5 minus the time period.\r<BR>\n" );
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document.write( "investment in time period 1 is multiplied by 1.06 ^ (5 - 1)<BR>\n" );
document.write( "investment in time period 2 is multiplied by 1.06 ^ (5 - 2)<BR>\n" );
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document.write( "investment in time period 5 is multiplied by 1.06 ^ (5 - 5)\r<BR>\n" );
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document.write( "the following excel printout shows the calculations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/010503.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "when working with the calculator, you use the percent interest rate.\r<BR>\n" );
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document.write( "when working with the formulas, you use the interest rate.\r<BR>\n" );
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document.write( "interest rate = percent interest rate / 100.\r<BR>\n" );
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document.write( "when working with the calculator, investments are negative because they're money going out.\r<BR>\n" );
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document.write( "what you get back is positive because it's money coming in.\r<BR>\n" );
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document.write( "the calculator will automatically make the present and future value negative if the payments are positive, and vice versa.\r<BR>\n" );
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document.write( "the value of the fund at the end of the investment period is the future value of the payments at 6% per year.\r<BR>\n" );
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