document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202728>Question 1202728</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have searched online and found banks offering two different interest rates for the same service: Bank A offers 4.5%/a and Bank B offers 4.9%/a. All other terms of the service are the same.\r<BR>\n" );
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document.write( "In what situation would you be better off choosing Bank B? Explain </SPAN>\n" );
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document.write( "It should be fairly clear that bank B is the better offer since 4.9% > 4.5%\r<BR>\n" );
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document.write( "You can think of it like saying 49 > 45.\r<BR>\n" );
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document.write( "Let's look at a slightly more complicated example.\r<BR>\n" );
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document.write( "Bank A offers 6.25% compounded daily.<BR>\n" );
document.write( "Bank B offers 6.30% compounded semi-annually.<BR>\n" );
document.write( "Which bank is the better deal?\r<BR>\n" );
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document.write( "The annual percentage yield (APY) formula is<BR>\n" );
document.write( "APY = (1 + APR/n)^n - 1\r<BR>\n" );
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document.write( "For bank A,<BR>\n" );
document.write( "APY = (1 + APR/n)^n - 1<BR>\n" );
document.write( "APY = (1 + 0.0625/365)^365 - 1<BR>\n" );
document.write( "APY = 0.06448876344422<BR>\n" );
document.write( "APY = 0.06449<BR>\n" );
document.write( "APY = 6.449%\r<BR>\n" );
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document.write( "And bank B,<BR>\n" );
document.write( "APY = (1 + APR/n)^n - 1<BR>\n" );
document.write( "APY = (1 + 0.063/2)^2 - 1<BR>\n" );
document.write( "APY = 0.06399225<BR>\n" );
document.write( "APY = 0.06399<BR>\n" );
document.write( "APY = 6.399%\r<BR>\n" );
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document.write( "Bank A offers the better APY even though 6.25% < 6.30% <BR>\n" );
document.write( "Bank A gets a bigger boost because the interest is compounded far more frequently.\r<BR>\n" );
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document.write( "This entire section is a hypothetical example of course.<BR>\n" );
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