document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190272>Question 1190272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you want to have $700,000 for retirement in 30 years. Your account earns 7% interest.\r<BR>\n" );
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document.write( "a) How much would you need to deposit in the account each month? (Round up to the dollar's place.)\r<BR>\n" );
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document.write( "b) How much interest will you earn? </SPAN>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "Future value of annuity formula<BR>\n" );
document.write( "FV = P*( (1+i)^n - 1 )/i<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "FV = future value<BR>\n" );
document.write( "P = periodic deposit<BR>\n" );
document.write( "i = interest rate per period<BR>\n" );
document.write( "n = number of periods\r<BR>\n" );
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document.write( "In this case,<BR>\n" );
document.write( "FV = 700,000<BR>\n" );
document.write( "P = unknown monthly deposit<BR>\n" );
document.write( "i = 0.07/12 = monthly interest rate<BR>\n" );
document.write( "n = 12*30 = 360 months\r<BR>\n" );
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document.write( "Let's plug in the values mentioned and solve for P<BR>\n" );
document.write( "FV = P*( (1+i)^n - 1 )/i<BR>\n" );
document.write( "700,000 = P*( (1+0.07/12)^360 - 1 )/(0.07/12)<BR>\n" );
document.write( "700,000 = P*1,219.97099577594<BR>\n" );
document.write( "P = (700,000)/(1,219.97099577594)<BR>\n" );
document.write( "P = 573.784132920946<BR>\n" );
document.write( "P = 573.78<BR>\n" );
document.write( "You need to deposit $573.78 per month, for 360 months, so that you end up with a future value of about $700,000.\r<BR>\n" );
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document.write( "Your teacher then states to round up to the nearest dollar. So we go from 573.78 to 574\r<BR>\n" );
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document.write( "Answer: <font color=red>$574</font>\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "If you plugged P = 574, i = 0.07/12, and n = 360 into the future value annuity formula, then you'd get roughly FV = 700,263.35\r<BR>\n" );
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document.write( "We don't hit $700,000 exactly, but instead go over a bit. <BR>\n" );
document.write( "The alternative is that if P = 573, then FV would be somewhat shy of the 700 thousand dollar goal.<BR>\n" );
document.write( "So this is why we rounded up.\r<BR>\n" );
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document.write( "Ignore the interest portion for now.<BR>\n" );
document.write( "If you made 360 deposits of $574 each, then you paid 360*574 = 206,640 dollars into the account.\r<BR>\n" );
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document.write( "The total interest is the difference of the results we got<BR>\n" );
document.write( "700,263.35 - 206,640 = 493,623.35\r<BR>\n" );
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document.write( "Answer: <font color=red>$493,623.35</font><BR>\n" );
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