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

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

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New post 03 Feb 2016, 10:41
BrainLab wrote:
butterfly wrote:
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


I also avoided the route of quadratic equations here. The first thing I asked myself, how much compound interest (approx). would be earned with an 8% interest rate.
If I invest $1,000, I will get $80 interest the first year, and $80 interest the second year, makes $160 in total. Compound interest on the interest earned during the first year is another 8% on $80, so $6.4.

In total I received interest of $166.4

(1) Deposit earns $210, that is clearly more than what I would get with 8% interest => Sufficient
(2) If it's not immediately obvious that this statement actually tells you that you earn more than 15% compound interest on the investment in 2 years, look closely at the given formula in the stem. This equals to $150 for the $1,000 investment. So the compound interest could be lower or higher compared to what I get with 8% => Insufficient

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

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New post 30 Jan 2017, 17:16
Bunuel wrote:
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.



Hello Bunuel,

Your solution is perfect but I am still confused that why this statement is insufficient because if at r =8 this condition is true 1.16>1.15(1+r100)2=(1+8100)2=1.082≈1.16>1.15, then at r>8 this condition will also be true hence confused with this.
Thanks in advance.
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Re: If $1,000 is deposited in a certain bank account and remains in the [#permalink]

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New post 25 Sep 2017, 07:33
Dear Experts Bunuel, VeritasPrepKarishma,

In case of inequalities, can we take square roots on both sides?
Thanks in advance.

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

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New post 25 Sep 2017, 07:43
Th3Ap3xPr3dator wrote:
Dear Experts Bunuel, VeritasPrepKarishma,

In case of inequalities, can we take square roots on both sides?
Thanks in advance.


We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality).

Check for more here: Manipulating Inequalities (adding, subtracting, squaring etc.).

Hope it helps.
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