document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190444>Question 1190444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A. For all parts of this problem, money is invested in a retirement account with an APR of 8.04%.  (This is close to the average annual return rate for a traditional individual retirement account over the last decade.)  You want to be able to withdraw $24,000 per year for 20 years after retirement.  Round up to the cent for each answer.<BR>\n" );
document.write( " How much must you have in the account to start with if compounding and withdrawals are both annual? </SPAN>\n" );
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document.write( "Present value of annuity<BR>\n" );
document.write( "PV = C*(1 - (1+i)^(-n))/i\r<BR>\n" );
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document.write( "C = amount of cash needed per period = $24,000<BR>\n" );
document.write( "i = interest rate per period = 0.0804<BR>\n" );
document.write( "n = number of periods = 20<BR>\n" );
document.write( "Each period is one year.\r<BR>\n" );
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document.write( "PV = C*(1 - (1+i)^(-n))/i<BR>\n" );
document.write( "PV = 24000*(1 - (1+0.0804)^(-20))/0.0804<BR>\n" );
document.write( "PV = 234,935.78356008<BR>\n" );
document.write( "PV = 234,935.78 \r<BR>\n" );
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document.write( "Interpretation:<BR>\n" );
document.write( "If you want 20 annual withdrawals of $24,000 spaced into the future, then you must have $234,935.78 currently today (aka present value). Those 20 future payments are equivalent this current present value payment. This is when we take into account the 8.04% interest rate, compounded annually.\r<BR>\n" );
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document.write( "Answer: $234,935.78<BR>\n" );
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