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If $1,000 is deposited in a certain bank account and remains

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If $1,000 is deposited in a certain bank account and remains [#permalink] New post 13 Nov 2009, 14:45
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If $1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of interest, I, earned by the deposit in the first n years is given by the formula I=1,000((1+r/100)^n-1), where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank greater than 8 percent?

(1) The deposit earns a total of $210 in interest in the first two years
(2) (1 + r/100 )^2 > 1.15

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-1-000-is-deposited-in-a-certain-bank-account-and-remains-104084.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 May 2014, 00:26, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Tough GMAT Prep DS: please help [#permalink] New post 13 Nov 2009, 16:46
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The answer is A.

The question asks:

If \(I = 1000*[(1+\frac{r}{100})^n - 1)]\), is r > 8%?

Essentially, you have 3 unknowns (I, r, and n), and you need to solve for r.

Statement 1: The deposit earns a total of $210 in interest in the first two years.

You are given I ($210) and n (2), and therefore can solve for r. Sufficient. If you want to actually solve for this, you can do so, but there really is no need for it.

Statement 2: \((1 + \frac{r}{100})^2 > 1.15\).

This is a bit more tricky. The above formula can be rearranged to the following:

\(1 + \frac{r}{100} > \sqrt{1.15}\)

Now assuming we don't have a calculator handy, you can mentally approximate this (erring on the side of being conservative) as:

\(r > 7.5%\) (It's actually less than this, but being conservative is fine)

We can make this approximation safely because, simply put, if r > 0, than \((1+r)^2 = 1 + 2r + r^2\) will always be greater than \((1 + 2r)\).

Since we need to know if r > 8%, this is insufficient.
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Re: Tough GMAT Prep DS: please help [#permalink] New post 13 Nov 2009, 21:11
Note that this is a YES/NO DS question. So finding the solution regardless of whether it is YES or NO is sufficient.

Statement 1

We are given both the value of I and the value of n. That is two out of the three variables in the formula given above. No further calculation is necessary. Again, because this is a YES/NO question, even if the value is less than 8 percent, you can still answer the question.

SUFFICIENT

Statement 2

Because the statement given is an inequality, we must solve the equation to determine whether it is sufficient. If the r given in the statement is greater than a value less than 8%, then we don't if that specific value of r is greater than or less than 8%.

(1+r/100)>(1.15)^(1/2)
1+r/100>1.07
r>.07

NOT SUFFICIENT

ANSWER: A.
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compound interest [#permalink] New post 13 Mar 2010, 00:09
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if $1,000 is deposited in a certain bank account and remains in the account along with any accrued interest, the dollar amount of interest, I, earned by deposit in the first n years is given by:

I = 1,000 ((1+r/100)^n -1)

where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank > 8%?

1) the deposit earns a total of $210 in interest in the first 2 years.

2) (1+r/100)^2 > 1.15
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Re: compound interest [#permalink] New post 13 Mar 2010, 01:57
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mustdoit wrote:
if $1,000 is deposited in a certain bank account and remains in the account along with any accrued interest, the dollar amount of interest, I, earned by deposit in the first n years is given by:

I = 1,000 ((1+r/100)^n -1)

where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank > 8%?

1) the deposit earns a total of $210 in interest in the first 2 years.

2) (1+r/100)^2 > 1.15


In other words we're asked whether \(r>8\).
Stat. 1: the deposit earns a total of $210 in interest in the first 2 years.
I replaced the "I" and "n" with the numbers from stat. 1:
\(210=(1+\frac{r}{100})^{2-1}\) - from this we can get "r" - sufficient.

Stat. 2: \((1+\frac{r}{100})^2>1.15\) \(=>\) \(1+\frac{r}{100}>\sqrt{1.15}\) \(=>\)
\(r>(\sqrt{1.15}-1)*100\) \(=>\) \(r>(\approx1.07-1)*100\) \(=>\) \(r>7\) - not sufficient

So, the answer is A. :wink:
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Re: compound interest [#permalink] New post 16 Mar 2010, 09:31
[quote="Igor010"]
Stat. 1: the deposit earns a total of $210 in interest in the first 2 years.
I replaced the "I" and "n" with the numbers from stat. 1:
\(210=(1+\frac{r}{100})^{2-1}\) - from this we can get "r" - sufficient.

[quote]

Isn't in statement 1 we do not have principle on which this interest was calculated. How can we assume it will be 1 only?
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Re: compound interest [#permalink] New post 16 Mar 2010, 09:57
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sidhu4u wrote:
Igor010 wrote:
Stat. 1: the deposit earns a total of $210 in interest in the first 2 years.
I replaced the "I" and "n" with the numbers from stat. 1:
\(210=(1+\frac{r}{100})^{2-1}\) - from this we can get "r" - sufficient.

Quote:

Isn't in statement 1 we do not have principle on which this interest was calculated. How can we assume it will be 1 only?

Sorry, don't understand your q. We have \(I=1000*(1+\frac{r}{100})^{n-1}\) as given and statement 1 gives us some figures to use in this formula... :?:
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Re: compound interest [#permalink] New post 16 Mar 2010, 11:22
Quote:
if $1,000 is deposited in a certain bank account and remains in the account along with any accrued interest, the dollar amount of interest, I, earned by deposit in the first n years is given by:

I = 1,000 ((1+r/100)^n -1)

where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank > 8%?

1) the deposit earns a total of $210 in interest in the first 2 years.

2) (1+r/100)^2 > 1.15



A quick look suggests both statements are correct unless you calculate interest rate in each case. Since statement 1 one will give a concrete value of r no need to calculate it, it's sufficient. BUT statement 2 needs calculation of r since r>1 or r>2 etc. these types of answers are not sufficient. r > 7.2%, not sufficient.
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Re: compound interest [#permalink] New post 18 Mar 2010, 21:27
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Igor010 wrote:
mustdoit wrote:
if $1,000 is deposited in a certain bank account and remains in the account along with any accrued interest, the dollar amount of interest, I, earned by deposit in the first n years is given by:

I = 1,000 ((1+r/100)^n -1)

where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank > 8%?

1) the deposit earns a total of $210 in interest in the first 2 years.

2) (1+r/100)^2 > 1.15


In other words we're asked whether \(r>8\).
Stat. 1: the deposit earns a total of $210 in interest in the first 2 years.
I replaced the "I" and "n" with the numbers from stat. 1:
\(210=(1+\frac{r}{100})^{2-1}\) - from this we can get "r" - sufficient.

Stat. 2: \((1+\frac{r}{100})^2>1.15\) \(=>\) \(1+\frac{r}{100}>\sqrt{1.15}\) \(=>\)
\(r>(\sqrt{1.15}-1)*100\) \(=>\) \(r>(\approx1.07-1)*100\) \(=>\) \(r>7\) - not sufficient

So, the answer is A. :wink:



Statement 1 is pretty easy to evaluate and you can get the answer...

About statement 2 we can do this way as well....

given \((1+\frac{r}{100})^2>1.15\)

this means we have received a interest greater than 15% ( 1+ .15) for 2 years. That could be 7.5 for each year (approx) or 10% for each year if the 1.15 figure becomes 1.21. Obviously we cannot confirm any value of R.

What do you say...??
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DS [#permalink] New post 10 May 2010, 16:40
29.If $1000 is deposited in a certain bank account and remains in the account along with any accumulated intrest, the dollar amount of intrest, I, earned by the deposit in the first n years is given by the formula I= 1000((1 + r/100)^n – 1), where r percent is the annual interest rate paid by the bank. Is the annual rate paid by the bank greater than 8 percent?

1.The deposit earns a total of $210 in interest in the first teo years.
2.(1 + r/100)^2 > 1.15

Thanks
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Re: Tough GMAT Prep DS: please help [#permalink] New post 03 Jul 2010, 13:28
Second option does not give a precise value of r as the one given by option one.
Thus A is the option that holds true.
Please post the OA.
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Re: If $1,000 is deposited in a certain bank account and remains [#permalink] New post 18 Jan 2012, 07:52
I calculated A too. But OA is given D.
In option 2 r>7.
Help please.
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Re: If $1,000 is deposited in a certain bank account and remains [#permalink] New post 18 Jan 2012, 07:59
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Baten80 wrote:
I calculated A too. But OA is given D.
In option 2 r>7.
Help please.


Answer is A. Discussed here: annual-interest-104084.html

If $1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of interest, I, earned by the deposit in the first n years is given by the formula I=1,000((1+r/100)^n-1), where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank greater than 8 percent?

Given: \(I=1,000((1+\frac{r}{100})^n-1)\). Question: is \(r>8\).


(1) The deposit earns a total of $210 in interest in the first two years --> \(I=210\) and \(n=2\) --> \(210=1,000((1+\frac{r}{100})^2-1)\) --> note that we are left with only one unknown in this equation, \(r\), and we'll be able to solve for it and say whether it's more than 8, so even withput actual solving we can say that this statement is sufficient.

(2) (1 + r/100 )^2 > 1.15 --> if \(r=8\) then \((1+\frac{r}{100})^2=(1+\frac{8}{100})^2=1.08^2\approx{1.16}>1.15\) so, if \(r\) is slightly less than 8 (for example 7.99999), \((1+\frac{r}{100})^2\) will still be more than 1.15. So, this statement is not sufficient to say whether \(r>8\).

Answer: A.

This topics is locked, so in case of any question please post it here: annual-interest-104084.html

Hope it helps.
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Re: If $1,000 is deposited in a certain bank account and remains   [#permalink] 18 Jan 2012, 07:59
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