document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190446>Question 1190446</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.\r<BR>\n" );
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document.write( "4. How much must you have in the account to start with if compounding and withdrawals are both monthly?<BR>\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 = $24,000/12 = $2,000<BR>\n" );
document.write( "i = interest rate per period = 0.0804/12 = 0.0067 exactly<BR>\n" );
document.write( "n = number of periods = 20*12 = 240 months<BR>\n" );
document.write( "Each period is one month.\r<BR>\n" );
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document.write( "PV = C*(1 - (1+i)^(-n))/i<BR>\n" );
document.write( "PV = 2000*(1 - (1+0.0067)^(-240))/0.0067<BR>\n" );
document.write( "PV = 238,398.570184098<BR>\n" );
document.write( "PV = 238,398.57\r<BR>\n" );
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document.write( "Interpretation:<BR>\n" );
document.write( "If you want 240 monthly withdrawals of $2,000 spaced into the future (aka $24,000 per year for 20 years), then you must have $238,398.57 currently today. Those 240 future payments are equivalent this current present value payment. This is when we take into account the 8.04% interest rate, compounded monthly.\r<BR>\n" );
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document.write( "Answer: <font color=red>$238,398.57</font><BR>\n" );
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