document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257741>Question 257741</A>: <I><SPAN STYLE=\"word-break: break-all;\"> suppose u start saving today for a $45000 down payment that you plan to make on a house in 5 years. Assume that you make no deposits into the account after the initial deposit. For the account described below, how much would you have to deposit now to reach for $45000 goal in 5 years.\r<BR>\n" );
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document.write( "an account with daily compounding and an APR of 4%\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 #189622 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=189622\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> daily compounding with annual interest rate of 4%.\r<BR>\n" );
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document.write( "formula is f = p * (1+r)^n\r<BR>\n" );
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document.write( "f = future value = 45000\r<BR>\n" );
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document.write( "p is what you're trying to find.\r<BR>\n" );
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document.write( "I believe daily compounding assumes 30 days each month totaling 360 days each year for financial purposes.\r<BR>\n" );
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document.write( "If you're not happy with this you can adjust to whatever days in the year you wish to have.\r<BR>\n" );
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document.write( "It won't make much of a difference either way.\r<BR>\n" );
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document.write( "r = 4% / 100% = .04 / 360 = .000111111\r<BR>\n" );
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document.write( "number of years is multiplied by 360 to get number of days.\r<BR>\n" );
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document.write( "you get 360 * 5 = 1800\r<BR>\n" );
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document.write( "n = number of time periods = 1800 days.\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "45000 = p * (1.00011111)^1800\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "45000 = p * 1221389186\r<BR>\n" );
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document.write( "solve for p to get:\r<BR>\n" );
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document.write( "p = 45000 / 1.221389186 = 36843.29329\r<BR>\n" );
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document.write( "you would have to invest $36,843.29 today to have $45,000 in 5 years at 4% per year compounded daily.\r<BR>\n" );
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document.write( "--------------------------------------\r<BR>\n" );
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document.write( "following information is interesting to know but not necessary to solve your problem.\r<BR>\n" );
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document.write( "that was solved above the dashed line.\r<BR>\n" );
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document.write( "additional interesting information:\r<BR>\n" );
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document.write( "this figure is very close to what you would get with continuous compounding.\r<BR>\n" );
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document.write( "with continuous compounding, the formula would be:\r<BR>\n" );
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document.write( "f = p * e^(r*t)\r<BR>\n" );
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document.write( "e is the scientific constant of 2.718281828...\r<BR>\n" );
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document.write( "r = .04<BR>\n" );
document.write( "t = 5 years\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "45000 = p * e^(.04*5)\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "45000 = p * 1.221402758\r<BR>\n" );
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document.write( "solve for p to get:\r<BR>\n" );
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document.write( "p = 45000 / 1.221402758 = 36842.88389.\r<BR>\n" );
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