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If $1,000 is deposited in a certain bank account and remains [#permalink]

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13 Nov 2009, 15:45

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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

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.

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%.

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.

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.

[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?
_________________

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...

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.

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.

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.

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

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 \(r>8\).

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