document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173770>Question 1173770</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A major city wants to establish a sinking fund to pay off debts of PKR 800 million which come due in 10 years. The city can earn interest at the rate of 8 percent per year compounded monthly. If first deposit is made 1 month from now;<BR>\n" );
document.write( "a)What monthly deposit will be required to accumulate the PKR 800 million?<BR>\n" );
document.write( "b)How much interest will be earned on these deposits<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 #850718 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=850718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the required monthly deposit and the total interest earned:\r<BR>\n" );
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document.write( "**a) Monthly Deposit**\r<BR>\n" );
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document.write( "* **Future Value (FV):** PKR 800,000,000<BR>\n" );
document.write( "* **Annual Interest Rate (r):** 8% or 0.08<BR>\n" );
document.write( "* **Number of Years (t):** 10<BR>\n" );
document.write( "* **Compounding Periods per Year (n):** 12 (monthly)\r<BR>\n" );
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document.write( "1.  **Calculate the Monthly Interest Rate (i):**<BR>\n" );
document.write( "    * i = r / n = 0.08 / 12 ≈ 0.006667\r<BR>\n" );
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document.write( "2.  **Calculate the Total Number of Periods (nt):**<BR>\n" );
document.write( "    * nt = n * t = 12 * 10 = 120\r<BR>\n" );
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document.write( "3.  **Use the Sinking Fund Formula:**<BR>\n" );
document.write( "    * PMT = FV * [i / ((1 + i)^nt - 1)]<BR>\n" );
document.write( "    * PMT = 800,000,000 * [0.006667 / ((1 + 0.006667)^120 - 1)]<BR>\n" );
document.write( "    * PMT ≈ 800,000,000 * [0.006667 / (2.219416 - 1)]<BR>\n" );
document.write( "    * PMT ≈ 800,000,000 * [0.006667 / 1.219416]<BR>\n" );
document.write( "    * PMT ≈ 800,000,000 * 0.005467<BR>\n" );
document.write( "    * PMT ≈ 4,373,600 PKR\r<BR>\n" );
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document.write( "Therefore, the city needs to deposit approximately **PKR 4,373,600** each month.\r<BR>\n" );
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document.write( "**b) Total Interest Earned**\r<BR>\n" );
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document.write( "1.  **Calculate the Total Amount Deposited:**<BR>\n" );
document.write( "    * Total Deposited = Monthly Deposit * Number of Payments<BR>\n" );
document.write( "    * Total Deposited = 4,373,600 * 120 = 524,832,000 PKR\r<BR>\n" );
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document.write( "2.  **Calculate the Total Interest Earned:**<BR>\n" );
document.write( "    * Total Interest = Future Value - Total Deposited<BR>\n" );
document.write( "    * Total Interest = 800,000,000 - 524,832,000 = 275,168,000 PKR\r<BR>\n" );
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document.write( "Therefore, the total interest earned will be approximately **PKR 275,168,000**.\r<BR>\n" );
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document.write( "**Using the provided code result to verify**\r<BR>\n" );
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document.write( "The code provided the results.<BR>\n" );
document.write( "Monthly deposit required: PKR 4372874.22<BR>\n" );
document.write( "Total interest earned: PKR 275255094.19\r<BR>\n" );
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document.write( "The answers are very close to the manually calculated answers. The small difference is due to rounding during the manual calculation.<BR>\n" );
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