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14 Aug 2021, 15:35
Kudos
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I would like some assistance with understanding Martha's portion of this problem.
Martha’s interest, 12%/12 = 1% each month:
For the 1st month = $100,000*0.01 = $1,000. Martha has $101,000 at the end of month 1
For the 2nd month = $101,000*1.01 ~ $102,000
For the 3rd month = $102,000*1.01 ~ $102,000+$1,020 ~ $103,000
The top post seems to only be calculating the interest on the interest ($1,000 + 1% of 1,000 = $1,010). In reality, the full amount will compound at the end of each month. I understand that this is an approximation, but only calculating the interest on the interest seems like too much of an approximation. What am I missing here?
Martha’s interest, 12%/12 = 1% each month:
For the 1st month = $100,000*0.01 = $1,000. Martha has $101,000 at the end of month 1
For the 2nd month = $101,000*1.01 ~ $102,000
For the 3rd month = $102,000*1.01 ~ $102,000+$1,020 ~ $103,000
The top post seems to only be calculating the interest on the interest ($1,000 + 1% of 1,000 = $1,010). In reality, the full amount will compound at the end of each month. I understand that this is an approximation, but only calculating the interest on the interest seems like too much of an approximation. What am I missing here?
11 Sep 2021, 20:40
Kudos
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We can use our common sense also compounding every month means annual effective rate would little bit more than 12% and less than 13 % so c would be the answere around 12.6%
we can solve this ques in just 20 seconds...
we can solve this ques in just 20 seconds...
20 Oct 2022, 09:11
Kudos
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Given: 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.
Asked: At the end of one full year, compared to Peter's account, approximately how much more does Martha’s account have?
Peter's interest at the end of the year = $100,000 * 12% = $12000
Matha's interest at the end of the year = $100,000 * {(1+12%/12)^12 - 1} = $100,000 *(1.01^12-1) = $100,000 (.12 + 12C2*.0001 + 12C3*.000001 ) = $12000 + $660 + $22
Difference in interest received by Peter and Martha at the end of the year = $682
IMO C
Asked: At the end of one full year, compared to Peter's account, approximately how much more does Martha’s account have?
Peter's interest at the end of the year = $100,000 * 12% = $12000
Matha's interest at the end of the year = $100,000 * {(1+12%/12)^12 - 1} = $100,000 *(1.01^12-1) = $100,000 (.12 + 12C2*.0001 + 12C3*.000001 ) = $12000 + $660 + $22
Difference in interest received by Peter and Martha at the end of the year = $682
IMO C
