document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172796>Question 1172796</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are the vice president of finance for a manufacturer of scuba diving gear. The company is planning a major plant expansion in 5 years. You have decided to start a sinking fund to accumulate the funds necessary for the project. Your company's investments yield 12% compounded quarterly. It is estimated that $3,000,000 in today's dollars will be required; however, the inflation rate on construction costs and plant equipment is expected to average 6% per year for the next 5 years.\r<BR>\n" );
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document.write( "A) Use the compound interest concept to determine how much (in $) will be required for the project, taking inflation into account.\r<BR>\n" );
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document.write( "B) What sinking fund payments (in $) will be required at the end of every 3-month period to accumulate the necessary funds?\r<BR>\n" );
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document.write( "For A, I used the compound interest formula of compound amount - principal. I got 1,040,580 and 2,418,330. Both answers were wrong.\r<BR>\n" );
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document.write( "For B, I used the sinking value formula: future value x i/(1+i)^n-1. My answers were 129,737.21 and 111,647.12\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 #797906 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=797906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you didn't say that either of your answers for B were correct or incorrect.<BR>\n" );
document.write( "let me give it a shot.\r<BR>\n" );
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document.write( "for A, the question is:\r<BR>\n" );
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document.write( "A) Use the compound interest concept to determine how much (in $) will be required for the project, taking inflation into account.<BR>\n" );
document.write( "inflation rate on construction costs and plan equipment is expected to average 6% per year for the next 5 years.<BR>\n" );
document.write( "3,000,000 * 1.06^5 = 4,014,676.733 in 5 years.<BR>\n" );
document.write( "because of inflation, the costs increase by 6% per year.\r<BR>\n" );
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document.write( "for B, the question is:\r<BR>\n" );
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document.write( "B) What sinking fund payments (in $) will be required at the end of every 3-month period to accumulate the necessary funds?\r<BR>\n" );
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document.write( "i used a financial calculator to answer this question.<BR>\n" );
document.write( "what i got was:<BR>\n" );
document.write( "the quarterly payment to the fund would have to be 149,409.04 dollars.\r<BR>\n" );
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document.write( "my inputs were:<BR>\n" );
document.write( "present value (pv) = 0<BR>\n" );
document.write( "future value (fv) = 4,014,676.733<BR>\n" );
document.write( "number of time periods (np) = 5 years * 4 quarters per year = 20 quarters.<BR>\n" );
document.write( "interest rate % per time period (ir) = 12% per year / 4 = 3% per quarter.<BR>\n" );
document.write( "payment is made at the end of each time period (beginning/end).\r<BR>\n" );
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document.write( "i then clicked on payment amount (pmt) and it told me that the amount of money to be invest at the end of each quarter is 149,409.04, as stated above.\r<BR>\n" );
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document.write( "i then looked at your formula.<BR>\n" );
document.write( "that formula is for future value, not for payments.<BR>\n" );
document.write( "so, to begin with, you used the wrong formula.<BR>\n" );
document.write( "the formula i have is in the following reference.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#formulas\" target = \"_blank\">https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#formulas</a><BR>\n" );
document.write( "the particular formula from  that  reference is shown below:\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( "in this formula, you use the rate per quarter, not the percent rate per quarter.\r<BR>\n" );
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document.write( "with a future amount of 4,014,676.733 (without the commas), and an interest rate of .03 per quarters and a number of time periods of 20, the formula becomes:\r<BR>\n" );
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document.write( "a = (f*r)/((1+r)^n-1) becomes:<BR>\n" );
document.write( "a = (4014676.733 * .03) / ((1+.03)^20-1)<BR>\n" );
document.write( "solve to get:<BR>\n" );
document.write( "a = 149409.0354\r<BR>\n" );
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document.write( "round that to 2 decimal places and it becomes 149409.04, same as i got with the financial calculator.\r<BR>\n" );
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document.write( "the results from the financial calculator are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/011005.jpg\" >\r<BR>\n" );
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document.write( "let me know if these answers get you to the right answer.<BR>\n" );
document.write( "i'll be very happy if they do.<BR>\n" );
document.write( "i'll be most interested in finding out what the correct answer is so i can figure out where i went wrong if they don't.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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