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If $1,000 will be deposited in a bank account and I is the d

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If $1,000 will be deposited in a bank account and I is the d

by doclkk » Wed Aug 12, 2009 9:21 am
If $1,000 will be deposited in a bank account and I is the dollar amount of interest earned from the original deposit, represented as I = 1000 {[(1 + r/100)^n] – 1}, and the annual interest rate is r percent, is r > 8 percent?
(1) The deposit earns a total of $210 in interest in the first 2 years.
(2) (1 + r/100)^2 > 1.15

(D)

What's the approach to this question?
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Source: — Data Sufficiency |
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by ashis979 » Wed Aug 12, 2009 11:32 am
Are you sure the answer is not A? I don't see how Stmt 2 is sufficient?

From the stem,
I=1,000[(1 + r/100)^n – 1]

Stmt 1: I = 210 in 2 years. You have the value for I and the value for n, you can plug this into the stem above and solve for r.....SUFFICIENT

Stmt 2: (1+r/100)^2>1.15
Taking the square root, (1+r/100)>sqrt(1.15)
Sqrt(1.15) is greater than 1 and less that 1.1 (1^2=1 and 1.1^2=1.21)
More precisely, it is between 1.05 and 1.1 (1.05^2 = 1.1025)
So the middle of the two numbers =1.075
Therefore, (1+r/100)>1.075=> (r/100)>0.075=> r>7.5
Since r can be anything greater than 7.5% like 7.6%, 7.7%, and we cannot determine if it is greater than 8%.....INSUFFICIENT

So the answer is A in my opinion. Please explain why you say the answer is D.
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