Peter takes a loan of $100,000 with 12% annual interest: the interest is paid once, at the end of the year. Martha takes a loan of $100,000 with 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Peter's loan interest, approximately how much more does Martha have to repay?  Options.
A) $68.25  B) Zero  C) $6825.00  D) $6.82  E) $682.50
Peters interest= $100,000*0.12 = $12,000 or $1,000 each month.   Martha’s interest, 12%/12 = 1% each month:   For the 1st month = $100,000*0.01 = $1,000;   For the 2nd month = $1,000 + 1% of 1,000 = $1,010, so we would have interest earned on interest (very small amount);   For the 3rd month = $1,010 + 1% of 1,010 = ~$1,020;   For the 4th month = $1,020 + 1% of 1,020 = ~$1,030;   ...   For the 12th month = $1,100 + 1% of 1,100 = ~$1,110.   The difference between Peters interest and Martha’s interest = ~(10 + 20 + ... + 110) = $660.   Answer: $682.50.
<result>E</result>
Peter takes a loan of $100,000 with 12% annual interest: the interest is paid once, at the end of the year. Martha takes a loan of $100,000 with 12% annual interest, compounding monthly at the end of each month. At the end of one full year, compared to Peter's loan interest, approximately how much more does Martha have to repay?