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The difference, after two years, between compound interest and simple

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The difference, after two years, between compound interest and simple  [#permalink]

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New post 27 Sep 2018, 05:35
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The difference, after two years, between compound interest and simple interest on a certain sum of money invested at the same rate of interest, is $18. If the simple interest accumulated on the sum after two years is $180, what is the rate of interest at which the sum of money was invested?

(A) 36%
(B) 30%
(C) 25%
(D) 20%
(E) 10%

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Re: The difference, after two years, between compound interest and simple  [#permalink]

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New post 27 Sep 2018, 12:32
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Bunuel wrote:
The difference, after two years, between compound interest and simple interest on a certain sum of money invested at the same rate of interest, is $18. If the simple interest accumulated on the sum after two years is $180, what is the rate of interest at which the sum of money was invested?

(A) 36%
(B) 30%
(C) 25%
(D) 20%
(E) 10%


We'll use the underlying logic behind interest to create a simple equation, without bothering with variables.
This is a Logical approach.

The only difference between the compound and simple interest is that the compound interest was calculated twice - once at the end of the first year and once at the end of the second year.
So, the $18 difference must be due to the second year's interest earned from the first year's interest.
Since 2 years of simple interest is $180, one year is $90 so 90*rate = 18 meaning that our interest rate is 18/90 = 2/10 = 20%

(D) is our answer.

Note that understanding the underlying logic created an extremely simple calculation: 18 divided by (180/2), as opposed to something full of variables.
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Re: The difference, after two years, between compound interest and simple  [#permalink]

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New post 28 Sep 2018, 04:53
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If simple interest was 180$, that means simple interest must have been 90$ per year. So, the difference in 18$ must have ocurred due to the interest in interest, i.e. (90*x)/100 = 18, x = 20%.

IMO D.
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Re: The difference, after two years, between compound interest and simple  [#permalink]

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New post 30 Sep 2018, 11:57
urvashis09

Can you please elaborate the explaination which you mentioned above.

I have on concern , $18 is for 2 year , how you can take $90*x/100 = $18
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The difference, after two years, between compound interest and simple  [#permalink]

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New post 30 Sep 2018, 22:03
vipulshahi wrote:
urvashis09

Can you please elaborate the explaination which you mentioned above.

I have on concern , $18 is for 2 year , how you can take $90*x/100 = $18


Sure, when you calculate simple interest and compound interest for any given amount, the interest for the first year remains the same. Example, you have 100$ on both SI and CI for 2 years @ 10%, for the first year both will earn an interest of 10$. But for the second year, SI will again earn 10$, but CI will earn 11$. Why? because now the amount for CI becomes the amount initially invested plus the interest earned i.e. 100$ + 10$ = 110$. Since the interest earned is not taken out but added in the principal amount invested for CI, the difference starts coming from second year onwards.

Hope that helps.
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The difference, after two years, between compound interest and simple &nbs [#permalink] 30 Sep 2018, 22:03
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