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If $500 is deposited into a savings account at an annual interest rate

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If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 12 Oct 2015, 22:26
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A
B
C
D
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Question Stats:

47% (01:58) correct 53% (02:13) wrong based on 207 sessions

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Re: If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 12 Oct 2015, 23:04
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Bunuel wrote:
If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years?

A) $750.00
B) $823.50
C) $973.25
D) $1000.25
E) $1100.00

Kudos for a correct solution.


ROI = 5% per annum compounded Monthly
Tenure, n = 10 years = 120 month
Principal = $500


5% per annum compounded monthly will be a little more than 5% at end of an year compounded anually = 6% per annum (approx)
in 10 yeasr the amoung simple rate will increase by 60% but at coumpound rate the amount wil increase more by 60%



This question can only be solved by approximation
60% of $500 = $300

i.e. amount after 10 years will be a little more than 500+300 = $800

i.e. B option seems the closest possible answer

Answer: option B
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Re: If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 12 Oct 2015, 23:58
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Bunuel wrote:
If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years?

A) $750.00
B) $823.50
C) $973.25
D) $1000.25
E) $1100.00

Kudos for a correct solution.


P = 500
R = 5% = 0.05
n = 12, no of times compounded in a year
t = 10, no of years

The formula is,

A = P * \((1 + \frac{R}{n})^{nt}\)

A = 500\((1 + \frac{0.05}{12})^{(12)(10)}\)

Total, A = 823.50 after 10 years.

Option B.
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Re: If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 13 Oct 2015, 04:59
The answer is B. Using the SI formula= 500*5/12*120/100=250
As CI will be slightly higher than that, the only value close enough is B.

Is this approach right Bunuel?
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Re: If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 13 Oct 2015, 05:16
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longfellow wrote:
The answer is B. Using the SI formula= 500*5/12*120/100=250
As CI will be slightly higher than that, the only value close enough is B.

Is this approach right Bunuel?


When you make pattern based or rule based statements, make sure that those statements are true for all possible cases.

You are right that CI will be slightly higher than that of a comparable SI but only after the 1st compounding. For the 1st compounding, SI=CI.

Hope this helps.
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Re: If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 13 Oct 2015, 05:55
Engr2012 wrote:
longfellow wrote:
The answer is B. Using the SI formula= 500*5/12*120/100=250
As CI will be slightly higher than that, the only value close enough is B.

Is this approach right Bunuel?


When you make pattern based or rule based statements, make sure that those statements are true for all possible cases.

You are right that CI will be slightly higher than that of a comparable SI but only after the 1st compounding. For the 1st compounding, SI=CI.

Hope this helps.



Thanks Engr2012!
Kudos+ for the quick turnaround time. :wave
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If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 13 Oct 2015, 06:18
Bunuel wrote:
If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years?

A) $750.00
B) $823.50
C) $973.25
D) $1000.25
E) $1100.00

Kudos for a correct solution.


\(500*(1+\frac{0.05}{12})^120\)=823,5
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Re: If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 21 May 2016, 10:37
shyind wrote:
Bunuel wrote:
If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years?

A) $750.00
B) $823.50
C) $973.25
D) $1000.25
E) $1100.00

Kudos for a correct solution.


P = 500
R = 5% = 0.05
n = 12, no of times compounded in a year
t = 10, no of years

The formula is,

A = P * \((1 + \frac{R}{n})^{nt}\)
A = 500\((1 + \frac{0.05}{12})^{(12)(10)}\)

Total, A = 823.50 after 10 years.

Option B.

Guyz....
how u people could calculate this(highlighted) fastely in real exam?????
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If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 21 May 2016, 10:48
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rohit8865 wrote:
how u people could calculate this(highlighted) fastely in real exam?????


IMHO the best approach for dealing with this problem has already been posted by GMATinsight

Use the simple interest problem , it's inhuman task to compute \(x^{120}\) under exam hall situation...


Basic understanding of the diff between SI and CI will help a lot here ( when options are widely apart )
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Re: If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 23 Jan 2017, 19:40
(1+x)^N for very small x and very large N can be approximated to (1+Nx).

So, 500(1+5/1200)^120 => 500(1+1/2) => 750. In this method ans comes out to be 750. Could someone chip in? Thanks!
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If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 07 Mar 2017, 10:38
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In case we have compound interest we can use rule of 70:

The rule of 70 is a way to estimate the number of years it takes for a certain variable to double. To estimate the number of years for a variable to double, take the number 70 and divide it by the growth rate of the variable.

So we divide 70 by 5 and receive approx 14 years
That means that in approx 14 years amount will be $1000
So after 10 years the amount should be higher than $750 and less than $1000

Only 2 options remain:
B and C

C is out, because it is too big
So correct is B
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Re: If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 12 Mar 2017, 11:43
if the annual rate for investment is 5% for 10year period it will be >50% since it is compounded monthly
hence 500*1,5=750<answer is more than 750, the closest would be 823
I wouldn't go for 973, since it's too many (if we take rule of 70 when it's needed (70/annual rate) years for investment to double
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Re: If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 11 Aug 2017, 20:02
Bunuel this is a really bad question..... i don't hope such questions are allowed to be posted on GMAT club and if the source says it is from Economist. I must say Economist has a very poor QA question collection.. Really sad to see such pathetic question.

GMAT would never test such guesswork. This question has one option $750 which is clearly wrong. After that all the options B,C,D,E are quite logically possible depending on the number of years we are taking or the interest. As the number of years increase or the rate of interest increase the multiplication factor of 60% or 70% assumed by people here will also increase.. Please remove such question from GMAT club.

Also my humble request is to not include such questions in the Daily Practice Questions. I am daily getting 1 or 2 useless questions out of 4 questions in PS/DS which fails the usability of such a good feature..

Though for a moment, the best answer is provided by GMATinsight but I really don't support such answers. Thanks.
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Re: If $500 is deposited into a savings account at an annual interest rate  [#permalink]

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New post 16 Aug 2018, 16:31
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Re: If $500 is deposited into a savings account at an annual interest rate   [#permalink] 16 Aug 2018, 16:31
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