document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190335>Question 1190335</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sandra deposits $3,000 at the beginning of each semiannual period for 12 years at 10% interest compounded semiannually. Determine the amount she will have in the account after 12 years. Round to the nearest cent.<BR>\n" );
document.write( "a.<BR>\n" );
document.write( "$130,506.00<BR>\n" );
document.write( "c.<BR>\n" );
document.write( "$121,291.43<BR>\n" );
document.write( "b.<BR>\n" );
document.write( "$140,181.30<BR>\n" );
document.write( "d.<BR>\n" );
document.write( "$70,568.14 </SPAN>\n" );
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document.write( "Apply the future value of annuity due formula (not the regular future value annuity).\r<BR>\n" );
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document.write( "The \"due\" is because each deposit is made at the beginning of the period. If the deposits were made at the end of the period, after the compounding gets a chance to happen, then we'd use a regular future value annuity formula.\r<BR>\n" );
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document.write( "The formula we use is<BR>\n" );
document.write( "FV = P(1+i)*( (1+i)^n - 1 )/i\r<BR>\n" );
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document.write( "where,<BR>\n" );
document.write( "FV = future value of the money after n periods<BR>\n" );
document.write( "P = deposit per period<BR>\n" );
document.write( "i = interest rate per period (in decimal form)<BR>\n" );
document.write( "n = number of periods\r<BR>\n" );
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document.write( "We have the following items<BR>\n" );
document.write( "P = 3000<BR>\n" );
document.write( "i = 0.10/2 = 0.05<BR>\n" );
document.write( "n = 2*12 = 24\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "FV = P(1+i)*( (1+i)^n - 1 )/i<BR>\n" );
document.write( "FV = 3000*(1+0.05)*( (1+0.05)^24 - 1 )/0.05<BR>\n" );
document.write( "FV = 140,181.296453963<BR>\n" );
document.write( "FV = <font color=red>$140,181.30</font><BR>\n" );
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