document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202559>Question 1202559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kalil and Bob each invest $550 every 3 months into an account through their employer. The interest compounds quarterly, and Kalil's work offers him a rate of 5.6%/a whereas Bob’s work offers him a rate of 5.2%/a.<BR>\n" );
document.write( "a) How much will Kalil and Bob each have saved up in 6 years?<BR>\n" );
document.write( "b) Who will earn more interest, and by how much?\r<BR>\n" );
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document.write( "<font color=red>Answers:</font><BR>\n" );
document.write( "(a) Kalil = $15,560.36 and Bob = $15,375.07<BR>\n" );
document.write( "(b) Kalil earns $185.29 more.\r<BR>\n" );
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document.write( "Work Shown for Part (a)\r<BR>\n" );
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document.write( "FV = future value<BR>\n" );
document.write( "P = periodic deposit or payment<BR>\n" );
document.write( "r = annual interest rate in decimal form <BR>\n" );
document.write( "i = quarterly interest rate in decimal form<BR>\n" );
document.write( "n = number of quarterly periods\r<BR>\n" );
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document.write( "1 quarter = 3 months\r<BR>\n" );
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document.write( "Future value of annuity formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+P%2A%28+%281%2Bi%29%5En+-+1+%29%2Fi ALIGN=MIDDLE  ALT=\"FV+=+P%2A%28+%281%2Bi%29%5En+-+1+%29%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For Kalil we have<BR>\n" );
document.write( "P = 550<BR>\n" );
document.write( "r = 0.056<BR>\n" );
document.write( "i = r/4 = 0.056/4 = 0.014 exactly<BR>\n" );
document.write( "n = 6*4 = 24 quarterly periods\r<BR>\n" );
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document.write( "Compute the future value (FV) for Kalil<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+P%2A%28+%281%2Bi%29%5En+-+1+%29%2Fi ALIGN=MIDDLE  ALT=\"FV+=+P%2A%28+%281%2Bi%29%5En+-+1+%29%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+550%2A%28+%281%2B0.014%29%5E24+-+1+%29%2F0.014 ALIGN=MIDDLE  ALT=\"FV+=+550%2A%28+%281%2B0.014%29%5E24+-+1+%29%2F0.014\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+15560.3633086689 ALIGN=MIDDLE  ALT=\"FV+=+15560.3633086689\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+15560.36 ALIGN=MIDDLE  ALT=\"FV+=+15560.36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Kalil will have $15,560.36 saved up.\r<BR>\n" );
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document.write( "Bob's input value for P and n will be the same.<BR>\n" );
document.write( "The key difference is that i = 0.052/4 = 0.013 exactly.\r<BR>\n" );
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document.write( "Compute the future value (FV) for Bob<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+P%2A%28+%281%2Bi%29%5En+-+1+%29%2Fi ALIGN=MIDDLE  ALT=\"FV+=+P%2A%28+%281%2Bi%29%5En+-+1+%29%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+550%2A%28+%281%2B0.013%29%5E24+-+1+%29%2F0.013 ALIGN=MIDDLE  ALT=\"FV+=+550%2A%28+%281%2B0.013%29%5E24+-+1+%29%2F0.013\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+15375.0668341114 ALIGN=MIDDLE  ALT=\"FV+=+15375.0668341114\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=FV+=+15375.07 ALIGN=MIDDLE  ALT=\"FV+=+15375.07\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Bob will have $15,375.07 in his account.\r<BR>\n" );
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document.write( "Work Shown for Part (b)\r<BR>\n" );
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document.write( "Each person deposits $550 per quarter, for 24 quarters (aka 6 years).<BR>\n" );
document.write( "Without interest that total deposit is 24*($550) = $13,200\r<BR>\n" );
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document.write( "Subtract this result from the results of part (a) to determine the interest earned.\r<BR>\n" );
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document.write( "Kalil =  $15,560.36 - $13,200 = $2,360.36<BR>\n" );
document.write( "Bob =  $15,375.07 - $13,200 = $2,175.07\r<BR>\n" );
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document.write( "Kalil earned more interest. This is to be expected since Kalil's annual rate is larger compared to Bob's rate. <BR>\n" );
document.write( "Both men have their money in their accounts for the same time frame, and same compounding frequency.\r<BR>\n" );
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document.write( "Subtract those results to see how big the gap is between the two.<BR>\n" );
document.write( "Kalil - Bob = $2,360.36 - $2,175.07 = $185.29\r<BR>\n" );
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document.write( "Kalil earned $185.29 more dollars compared to Bob.<BR>\n" );
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