document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101525>Question 1101525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A paper company is considering the purchase of a forest that is estimated to yield an annual return of $60,000 for 8 years, after which the forest will have no value. The company wants to earn 6% on its investment and also set up a sinking fund to replace the purchase price. If money is placed in the fund at the end of year and earns 4% compounded annually, find the yearly payment. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716147 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=716147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the forest yields an annual return of 60,000 for a period of 8 years.<BR>\n" );
document.write( "at the end of the 8 year period, the forest has no further value.\r<BR>\n" );
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document.write( "the company wants to earn 6% on its initial investment and also wants to set up a sinking fund to replace the purchase price.\r<BR>\n" );
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document.write( "if money is placed in the fund at the end of each year and earns 4% compounded annually, find the yearly payment.\r<BR>\n" );
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document.write( "the present value of the investment is the present value of 60,000 annual payments at the end of each year at 6% compounded annually.\r<BR>\n" );
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document.write( "the present value is therefore equal to $372,587.63 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "that's the amount that you have to invest initially.<BR>\n" );
document.write( "this amount will return 60,000 per year for 8 years if it earns 6% a year on that investment.\r<BR>\n" );
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document.write( "if you want to replace the purchase price at the end of the 8 year period and are making payments at 4% per year compounded annually, then you would have to put $40,436.13 into the fund at the end of each year.\r<BR>\n" );
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document.write( "you can use a financial calculator to do this, or you can use manual formulas.\r<BR>\n" );
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document.write( "if you are using a calculator, you would do something like the following:\r<BR>\n" );
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document.write( "to determine the initial investment:\r<BR>\n" );
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document.write( "present value (pv) = 0<BR>\n" );
document.write( "future value (fv) = 0<BR>\n" );
document.write( "number of time periods (ntp or np) = 8<BR>\n" );
document.write( "interest rate percent per time period (r%) = 6<BR>\n" );
document.write( "payments per time period (pmt) = 60000<BR>\n" );
document.write( "payments are set to be made at the end of each time period.\r<BR>\n" );
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document.write( "you would then have the calculator find the present value for you by clicking on the PV button.<BR>\n" );
document.write( "the present value will be negative because that's what you shell out initially.<BR>\n" );
document.write( "the payments will be positive because that's what you get back at the end of each time period.\r<BR>\n" );
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document.write( "i used an online calculator to show you.\r<BR>\n" );
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document.write( "these are your inputs:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/111501.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "this is the output.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/111502.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "to determine how much you have to invest at the end of each year in order to replace the original purchase price:\r<BR>\n" );
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document.write( "present value (pv) = 0<BR>\n" );
document.write( "future value (fv) = 372587.63<BR>\n" );
document.write( "number of time periods (ntp or np) = 8<BR>\n" );
document.write( "interest rate percent per time period (r% or ir%) = 4<BR>\n" );
document.write( "payments are set to be made at the end of each time period.\r<BR>\n" );
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document.write( "you would then have the calculator find the payment for you by clicking on the PMT button.<BR>\n" );
document.write( "the future value will be positive because that's what you get back.<BR>\n" );
document.write( "the payments will be negative because that's what you shell out at the end of each time period.\r<BR>\n" );
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document.write( "these are your inputs:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/111503.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "this is your output.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/111504.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "if you choose to use manual formulas, then the following reference will guide you.\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 particular formula you would use to find the initial investment 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 particular formula you would use to find the annual payments is:\r<BR>\n" );
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document.write( "ANNUITY FOR A FUTURE AMOUNT WITH END OF TIME PERIOD PAYMENTS \r<BR>\n" );
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document.write( "a = (f*r)/((1+r)^n-1) \r<BR>\n" );
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document.write( "a is the annuity.<BR>\n" );
document.write( "f is the future amount.<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( "when you use these formulas:\r<BR>\n" );
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document.write( "the interest rate per time period is not the percent.<BR>\n" );
document.write( "it is the decimal eqivalent of the percent.<BR>\n" );
document.write( "6% would become .06<BR>\n" );
document.write( "4% would become .04\r<BR>\n" );
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document.write( "also, you enter all values as positive.<BR>\n" );
document.write( "none of this negative positive business that is used with the financial calculators.\r<BR>\n" );
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document.write( "you can use your scientific calculator to solve these formulas.<BR>\n" );
document.write( "just make sure you use the parentheses exactly as shown.\r<BR>\n" );
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document.write( "i confirmed both formulas will give you the same results that the financial calculators gave you.\r<BR>\n" );
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document.write( "as an exercise, you can do the same confirmation yourself.\r<BR>\n" );
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document.write( "let me know if you have any difficulty getting the same results manually,or understanding what transpired.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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