guerrero25
Peter invests $100,000 in an account that pays 12% annual interest: the interest is paid once, at the end of the year. Martha invests $100,000 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 Peter's account, approximately how much more does Martha’s account have?
A. Zero
B. $68.25
C. $682.50
D. $6825.00
E. $68250.00
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: C.
Hope it helps.