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Help: DS Question on Interests

by praveen_gmat » Wed Aug 04, 2010 12:16 am
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 greater than
> 8%?

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

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

Please help me to solve the question in the quickest possible time.
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by Rahul@gurome » Wed Aug 04, 2010 2:10 am
First consider (1) alone.
210 = 1000((1+r/100)^2-1)
Or 210/1000 + 1 = (1+r/100)^2.
Or 121/100 = (1+r/100)^2
Or (1+r/100) = 11/10
Or r = 10% > 8%.
Or answer is yes.
So (1) alone is sufficient.

Next consider (2) alone.
(1+r/100)^2 > 1.15
Or (1+r/100) > sqrt(1.15)
Or (1+r/100) > 1.072
Or r/100 > 0.072
Or r > 7.2
But we cannot say definitely whether r is > 8 or not.
So (2) alone is not sufficient.

The correct answer is (A).
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by praveen_gmat » Wed Aug 04, 2010 2:14 am
Rahul@gurome wrote:First consider (1) alone.
210 = 1000((1+r/100)^2-1)
Or 210/1000 + 1 = (1+r/100)^2.
Or 121/100 = (1+r/100)^2
Or (1+r/100) = 11/10
Or r = 10% > 8%.
Or answer is yes.
So (1) alone is sufficient.

Next consider (2) alone.
(1+r/100)^2 > 1.15
Or (1+r/100) > sqrt(1.15)
Or (1+r/100) > 1.072
Or r/100 > 0.072
Or r > 7.2
But we cannot say definitely whether r is > 8 or not.
So (2) alone is not sufficient.

The correct answer is (A).

Hi Rahul,
Thanks for the response.. I understood your solution. However, when I solved, I could not do the sqrt(1.15) ..
Do you have any method to solve sqrt(1.15) or such numbers, in quick time .. ?
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by selango » Wed Aug 04, 2010 2:20 am
we can do it in another approach.

(1+r/100)^2 > 1.15

r>8?

Sub r=8

(1+8/100)^2>1.15

Sub r=9

(1+9/100)^2>1.15

r>=8

Insuff
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by Rahul@gurome » Wed Aug 04, 2010 7:08 am
Hi Praveen,
For getting the exact value of sqrt(1.15), it is better if you follow the usual division method.
However you can roughly estimate the range of sqrt(1.15) by the following method.
Select 2 perfect squares, 1 less than and 1 more than 1.15.
Now 1 < 1.15 < 1.21
Or sqrt(1) < sqrt(1.15) < sqrt(1.21)
Or 1 < sqrt(1.15) < 1.1
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