document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200973>Question 1200973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Carter expects to live for 30 years more after his retirement. He would like to withdraw $120,000 every year from his investment account (Account A) to pay for his living expenses. Carter’s investment account (Account A) pays 5% interest per year.<BR>\n" );
document.write( "How much money (a lump-sum) will Carter required to deposit in Account A at the beginning of his retirement (at age 60) to pay for his living expenses if<BR>\n" );
document.write( "(i) Account A start to pay interest one year after his retirement?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848048 by </B><A HREF=/tutors/aboutme.mpl?userid=asinus><B>asinus(45)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=asinus><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848048\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly, let's calculate the required initial deposit for Carter's retirement account.\r<BR>\n" );
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document.write( "**Understanding the Scenario**\r<BR>\n" );
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document.write( "* **Annual Withdrawal:** $120,000<BR>\n" );
document.write( "* **Interest Rate:** 5% per year<BR>\n" );
document.write( "* **Retirement Years:** 30 years<BR>\n" );
document.write( "* **Interest Payment Start:** One year after retirement\r<BR>\n" );
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document.write( "**Calculation**\r<BR>\n" );
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document.write( "Since the interest starts paying one year after retirement, we can use the formula for the present value of an ordinary annuity:\r<BR>\n" );
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document.write( "* **Present Value of Annuity = Annual Withdrawal * [(1 - (1 + Interest Rate)^(-Number of Years)) / Interest Rate]**\r<BR>\n" );
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document.write( "Substituting the values:\r<BR>\n" );
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document.write( "* Present Value of Annuity = $120,000 * [(1 - (1 + 0.05)^(-30)) / 0.05]<BR>\n" );
document.write( "* Present Value of Annuity = $120,000 * [(1 - 0.231377) / 0.05]<BR>\n" );
document.write( "* Present Value of Annuity = $120,000 * [0.768623 / 0.05]<BR>\n" );
document.write( "* Present Value of Annuity = $120,000 * 15.37246<BR>\n" );
document.write( "* Present Value of Annuity = $1,844,694.12\r<BR>\n" );
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document.write( "**Therefore, Carter will need to deposit $1,844,694.12 at the beginning of his retirement to cover his living expenses for 30 years.**\r<BR>\n" );
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document.write( "Let me know if you have any other questions or would like to explore different scenarios!<BR>\n" );
document.write( " </SPAN>\n" );
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