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Sarah invested $38,700 in an account that paid 6.2% annual interest

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Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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New post 12 Mar 2014, 20:31
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Question Stats:

54% (01:57) correct 46% (01:52) wrong based on 166 sessions

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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

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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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New post 12 Mar 2014, 22:41
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enigma123 wrote:
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

Any idea how to do this question please?



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.
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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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New post 12 Mar 2014, 20:59
2
1% of 38700 is 387
6% is approximately 2400
At the end of first year, total amount = 38700+2400 = 41000 (approx)
At the end of second year, total amount = 41000+2400 (6% of 41000 works out to approximately the same) = 43400 (approx)

So total earnings for third year cannot be more than 6% of 43400 i.e at max $3000
So monthly earning has to be in the range of 250.

Answer is A.
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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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New post 01 Feb 2016, 18:25
Nice Sum :D
Calculating simple interest for a month will be enough.
The compound interest for a month will be nearer to it but a little larger that the result
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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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New post 04 Feb 2016, 11:31
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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.

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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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New post 04 Feb 2016, 15:09
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.[/quote]

Hi,

I do not understand the highlighted above? why did you assume 7%
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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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New post 04 Feb 2016, 19:37
1
Mo2men wrote:
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.


Hi,

I do not understand the highlighted above? why did you assume 7%[/quote]

The given annual interest rate is 6.2% but the interest is compounded monthly. This means that the effective interest rate will be more than 6.2%. The integer after 6.2% is 7% so I approximated the effective interest rate to be 7%. It is more than what the actual effective annual interest rate will be (around 6.4%) but then, we intend to calculate simple interest and not compounded for 3 yrs hence a higher rate is justified. Note that our approximated answer (235) is very close to the actual answer (239.47).
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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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New post 14 Apr 2016, 01:35
VeritasPrepKarishma wrote:
enigma123 wrote:
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

Any idea how to do this question please?



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.



"EVEN iF THE ANSWERS CHOICES WERE CLOSER "
Hmm Makes me wonder =>
How about 278
279
280
281
290
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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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New post 14 Apr 2016, 04:45
1
stonecold wrote:
VeritasPrepKarishma wrote:
enigma123 wrote:
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

Any idea how to do this question please?



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.



"EVEN iF THE ANSWERS CHOICES WERE CLOSER "
Hmm Makes me wonder =>
How about 278
279
280
281
290


The correct answer is 239.47 which your options don't have. Besides, you are not given a calculator in the Quant section of GMAT so you are not expected to do tedious calculations. All I meant to say was that even if options were like 210, 240, 270 ... etc, you could have got the answer. Without a calculator, you will not be expected to calculate anything closer.
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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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New post 07 May 2017, 12:37
6.5%/12 = .54% or .5%
38700*5/1000=200 approx
(1+.005)^35= 1.xxx approx
200*1.xxx<714
answer:A
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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest  [#permalink]

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Re: Sarah invested $38,700 in an account that paid 6.2% annual interest &nbs [#permalink] 13 May 2018, 03:37
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