Sam invests $1000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Kody invests $1000 in an account that pays 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Sam's account, approximately how much more does Kody’s account have?
Answers:
A) Zero  B) $682.5  C) $68.25  D) $6.825  E) $0.6825
Sam's interest= $1000*0.12= 
<gadget id="calculator">1000*0.12</gadget>
<output>120</output>
$120 or $10 each month.   Kody’s interest, 12%/12= 1% each month:   For the 1st month = $1000*0.01= 
<gadget id="calculator">1000*0.01</gadget>
<output>10</output>
$10;   For the 2nd month= $10 + 1% of 10 = $10.1, so we would have interest earned on interest (very small amount);   For the 3rd month = $10.1 + 1% of 10.1 = ~$10.2;   For the 4th month = $10.201 + 1% of 10.201 = ~$10.3;   ...   For the 12th month = $11+ 1% of 11 = ~$11.1.   The difference between Sam's interest and Kody’s interest = ~(0.10 + 0.20 + ... + 1.10) = $6.6.   Answer: $6.825.
<result>D</result>
Sam invests $1000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Kody invests $1000 in an account that pays 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Sam's account, approximately how much more does Kody’s account have?