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12 Mar 2014, 21:31
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
54% (02:18) correct
46%
(02:34)
wrong
based on 558
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Sarah invested $38,700 in an account that paid 6.2% annual interest, compounding monthly. She left the money in this account, collecting interest for three full years. Approximately how much interest did she earn in the last month of this period?
A) $239.47
B )$714.73
C) $2793.80
D) $7,888.83
E) $15,529.61
A) $239.47
B )$714.73
C) $2793.80
D) $7,888.83
E) $15,529.61
12 Mar 2014, 23:41
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enigma123
The numbers are far too complicated so obviously you are expected to approximate a lot. That is the reason the options are so far apart.
With the given options, it is obvious that monthly interest rate will be about 6.2/12 = .5%
.5% of 38,700 will be less than 200 (since 1% is 387) and hence the monthly interest earned after 3 yrs can only be option (A). All other options are far too large.
Assume options were a little closer.
P = 38,700
Annual Interest = 6.2%
Since the interest is compounded monthly, the effective annual rate will be higher. Let's assume it is something close to 7%. The easiest interest calculation is using simple interest. If the interest was accumulated using SI at 7%, in 3 yrs, we would have accumulated about 20% of 38,700 which is one fifth of 38,700, say about 8000. This brings the total amount up to about 47000 at the end of 3 yrs. In the last month, the interest will be calculated on this figure since it is compounded.
The monthly interest rate will be 6.2/12 = .5% approximately.
.5% of 47000 will be about 235 (since 1% will be 470).
Answer (A)
Even if the options were a little closer, this method would have led you to the correct answer.
04 Feb 2016, 12:31
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Hi All,
While this question 'looks' complex, the answer choices to this question are so 'spread out' that you avoid almost all of the math and use logic to get the correct answer.
We're told that Sarah invested $38,700 in an account that paid 6.2% ANNUAL interest, compounded MONTHLY, for three full years. We're asked approximately how much interest she earned in the last month of this period.
As an aside, for a question that asks for an 'approximate' answer, these answers are far too exact. The GMAT would present these answers differently. That having been said, here's how you can answer this question relatively quickly:
With an annual interest rate of 6.2% and 12 monthly compounding periods per year, the account would receive about....
6%/12 = 0.5% interest per month.
1% of $38,700 = $387, so....
.5% of $38,700 = about $193
Over time, 'compounding' would take effect, so each monthly interest increase would be SLIGHTLY higher than the one that preceded it. This is meant to say that the original $193 would increase in really small increments over those 3 years, so there's really only one answer that makes sense.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
While this question 'looks' complex, the answer choices to this question are so 'spread out' that you avoid almost all of the math and use logic to get the correct answer.
We're told that Sarah invested $38,700 in an account that paid 6.2% ANNUAL interest, compounded MONTHLY, for three full years. We're asked approximately how much interest she earned in the last month of this period.
As an aside, for a question that asks for an 'approximate' answer, these answers are far too exact. The GMAT would present these answers differently. That having been said, here's how you can answer this question relatively quickly:
With an annual interest rate of 6.2% and 12 monthly compounding periods per year, the account would receive about....
6%/12 = 0.5% interest per month.
1% of $38,700 = $387, so....
.5% of $38,700 = about $193
Over time, 'compounding' would take effect, so each monthly interest increase would be SLIGHTLY higher than the one that preceded it. This is meant to say that the original $193 would increase in really small increments over those 3 years, so there's really only one answer that makes sense.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
