document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185511>Question 1185511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 1,200,000 pesos machine was purchased by a company. The said machine has an anticipated economic life of 5 years with a salvage value of 80,000 pesos given that the annual rate of inflation is 7% during the next 5 years. The machine will then be replaced with the same new machine and the company will accumulate the necessary capital by making equal end-of-year deposits in a reserve fund that earns 6% per annum. Determine the amount of actual deposit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849690 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the amount of the annual deposit:\r<BR>\n" );
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document.write( "1. **Calculate the future cost of the replacement machine:**\r<BR>\n" );
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document.write( "The cost of the machine increases due to inflation.  We use the future value formula:\r<BR>\n" );
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document.write( "Future Cost = Present Cost * (1 + Inflation Rate)^Economic Life\r<BR>\n" );
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document.write( "Future Cost = 1,200,000 * (1 + 0.07)^5<BR>\n" );
document.write( "Future Cost = 1,200,000 * 1.40255<BR>\n" );
document.write( "Future Cost ≈ 1,683,062.08 pesos\r<BR>\n" );
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document.write( "2. **Calculate the amount to be accumulated:**\r<BR>\n" );
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document.write( "The company needs to accumulate the future cost of the machine, less the salvage value of the old machine:\r<BR>\n" );
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document.write( "Amount to Accumulate = Future Cost - Salvage Value<BR>\n" );
document.write( "Amount to Accumulate = 1,683,062.08 - 80,000<BR>\n" );
document.write( "Amount to Accumulate ≈ 1,603,062.08 pesos\r<BR>\n" );
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document.write( "3. **Calculate the annual deposit:**\r<BR>\n" );
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document.write( "We use the future value of an ordinary annuity formula to find the equal end-of-year deposits needed:\r<BR>\n" );
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document.write( "FV = A * [(1 + i)^n - 1] / i\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* FV = Future Value (the amount to accumulate) = 1,603,062.08 pesos<BR>\n" );
document.write( "* A = Annual Deposit (what we want to find)<BR>\n" );
document.write( "* i = Interest rate = 0.06<BR>\n" );
document.write( "* n = Number of periods = 5 years\r<BR>\n" );
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document.write( "Rearranging the formula to solve for A:\r<BR>\n" );
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document.write( "A = FV * i / [(1 + i)^n - 1]\r<BR>\n" );
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document.write( "A = 1,603,062.08 * 0.06 / [(1 + 0.06)^5 - 1]<BR>\n" );
document.write( "A = 96,183.7248 / [1.3382255776 - 1]<BR>\n" );
document.write( "A = 96,183.7248 / 0.3382255776<BR>\n" );
document.write( "A ≈ 284,377.44 pesos\r<BR>\n" );
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document.write( "**Therefore, the amount of the actual deposit is approximately 284,377.44 pesos.**<BR>\n" );
document.write( " </SPAN>\n" );
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