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Peter invests $100,000 in an account that pays 12% [#permalink]

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21 Feb 2014, 07:11

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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

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.

Thanks Bunuel. I just wanted to tell Manofsteel that in as much as its a correct formula, that approach will waste a lot of time. Thanks for alternative, fast approach Bunuel.

Thanks Bunuel. I just wanted to tell Manofsteel that in as much as its a correct formula, that approach will waste a lot of time. Thanks for alternative, fast approach Bunuel.

To practice similar questions please follow the links in my post above.
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Re: Peter invests $100,000 in an account that pays 12% [#permalink]

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13 Jan 2015, 15:31

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Bunuel wrote:

guerrero25 wrote:

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.

Dear Bunuel, In the second month of Martha why didn't you pick the primary amount which is 100,000 . I mean at first month her interest is on 100,000 and second month it should be on 101,000 ? But you wrote on 1000. I am not clear actually. Can you please give a brief?

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.

Dear Bunuel, In the second month of Martha why didn't you pick the primary amount which is 100,000 . I mean at first month her interest is on 100,000 and second month it should be on 101,000 ? But you wrote on 1000. I am not clear actually. Can you please give a brief?

Your way: 0.01*$101,000 = $1,010. My way: $1,000 + 1% of 1,000 = $1,010.
_________________

Re: Peter invests $100,000 in an account that pays 12% [#permalink]

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20 Jan 2016, 11:25

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