document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207266>Question 1207266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A father is planning a savings program to put his daughter through college.<BR>\n" );
document.write( "His daughter is now 13 years old. She plans to enroll at the university in five<BR>\n" );
document.write( "years, and it should take her four years to complete her education. Currently,<BR>\n" );
document.write( "the cost per year (for everything—food, clothing, tuition, books, transportation, and so forth) is $12,500, but these costs are expected to increase by<BR>\n" );
document.write( "5 percent—the inflation rate—each year. The daughter recently received<BR>\n" );
document.write( "$7,500 from her grandfather’s estate; this money, which was invested in a<BR>\n" );
document.write( "mutual fund that pays 8 percent interest compounded annually, will be used<BR>\n" );
document.write( "to help meet the costs of the daughter’s education. The rest of the costs will<BR>\n" );
document.write( "be met by money that the father will deposit in a savings account. He will<BR>\n" );
document.write( "make equal deposits to the account in each year beginning today until his<BR>\n" );
document.write( "daughter starts college—that is, he will make a total of six deposits. These<BR>\n" );
document.write( "deposits will also earn 8 percent interest.<BR>\n" );
document.write( "a. What will be the present value of the cost of four years of education at the<BR>\n" );
document.write( "time the daughter turns 18? (Hint: Calculate the cost [at 5 percent inflation,<BR>\n" );
document.write( "or growth] for each year of her education, discount three of these costs back<BR>\n" );
document.write( "[at 8 percent] to the year in which she turns 18, then sum the four costs,<BR>\n" );
document.write( "which include the cost of the first year.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845041 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=845041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the annual cost of college is inflating at 5% per year.<BR>\n" );
document.write( "she is now 13.<BR>\n" );
document.write( "she will be 18 when she starts college.<BR>\n" );
document.write( "18 - 15 = 5 year from now.\r<BR>\n" );
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document.write( "the cost of college today is 12500 a year.<BR>\n" );
document.write( "5 years from now it will be 12500 * 1.05 ^ 5 = 15953.51953<BR>\n" );
document.write( "6 years from now it will be 12500 * 1.05 ^ 6 = 16751.19551<BR>\n" );
document.write( "7 years from mow it will be 12500 * 1.05 ^ 7 = 17588.75528<BR>\n" );
document.write( "8 years from now it will be 12500 * 1.05 ^ 8 = 18468.19305\r<BR>\n" );
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document.write( "the present value of those college costs will be the 5th year expense plus the 6th year expense / 1.08 plus the 7th year expense / 1.08 ^ 2 plus the 8th year expense / 1.08 ^ 3 = 61204.05552.\r<BR>\n" );
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document.write( "that's the amount of money she would need to have by the start of college which is at the end of year 5.<BR>\n" );
document.write( "note that end of year 5 is the beginning of year 6.\r<BR>\n" );
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document.write( "she needs to have 61204.05552 by the end of year 5.<BR>\n" );
document.write( "that's the present value of her college expenses for 4 years.\r<BR>\n" );
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document.write( "she has 7500 in savings today that is earning at the rate of 8% per year.<BR>\n" );
document.write( "at the end of year 5, that money will be equal to 7500 * 1.08 ^ 5 = 11019.96058.\r<BR>\n" );
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document.write( "the present value of her college costs minus that will be equal to 61204.05552 minus 11019.96058 = 50184.09494.\r<BR>\n" );
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document.write( "that's how much her father needs to each year starting at end of year 0 and ending at end of year 5.\r<BR>\n" );
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document.write( "end of year 0 is now.\r<BR>\n" );
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document.write( "the amount he needs to deposit each year is equal to 6334.133598.<BR>\n" );
document.write( "if he does that, he will have 50184.09495 at the end of the 6 payment investment period.\r<BR>\n" );
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document.write( "50184.09495 plus 11019.96058 in savings adds up to 61204.05552 which is the present value of her college costs at the end of year 5.\r<BR>\n" );
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document.write( "the spreadsheet page shown below has all the calculations in it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/051201.jpg\">\r<BR>\n" );
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document.write( "i haven't had time to explain this as fully as i would like, but i will be available to answer any questions you might have regarding my solution and how it was derived.\r<BR>\n" );
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document.write( "the calculation of the payments for the future value required for the father's investment is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/051203.jpg\">\r<BR>\n" );
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document.write( "that display is from the financial calculator at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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