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The compound interest on a certain sum of money invested at a certain

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The compound interest on a certain sum of money invested at a certain rate of interest in the 2nd year and in the 3rd year was $600 and $720 respectively. What was the rate of interest at which the sum of money was invested?

(A) 12.0%
(B) 12.5%
(C) 15.0%
(D) 20.0%
(E) 25.0%
[Reveal] Spoiler: OA

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Given :
On a given sum of money invested at a certain rate of interest,
Compound interest earned(2nd year) = 600$
Compound interest earned(3rd year) = 720$

Since, he has to include the 600$ earned during the second year,
while doing the calculations of the interest for the 3rd year, the additional compound interest earned = x% of 600.
Additional interest which is \(120$ =\frac{x}{100}* 600 => x =\frac{120}{6} = 20\)

Rate at which the sum was invested(x) = 20(Option D)
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Re: The compound interest on a certain sum of money invested at a certain [#permalink]

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Bunuel wrote:
The compound interest on a certain sum of money invested at a certain rate of interest in the 2nd year and in the 3rd year was $600 and $720 respectively. What was the rate of interest at which the sum of money was invested?

(A) 12.0%
(B) 12.5%
(C) 15.0%
(D) 20.0%
(E) 25.0%


\(ROI\) = \(\frac{720 - 600}{600}*100\)

So, \(ROI\) = \(\frac{120}{600}*100\)

Or, \(ROI\) = \(20\) %

Thus, the answer must be (D) 20 %
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Re: The compound interest on a certain sum of money invested at a certain [#permalink]

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New post 02 Jul 2017, 06:02
Abhishek009 wrote:
Bunuel wrote:
The compound interest on a certain sum of money invested at a certain rate of interest in the 2nd year and in the 3rd year was $600 and $720 respectively. What was the rate of interest at which the sum of money was invested?

(A) 12.0%
(B) 12.5%
(C) 15.0%
(D) 20.0%
(E) 25.0%


\(ROI\) = \(\frac{720 - 600}{600}*100\)

So, \(ROI\) = \(\frac{120}{600}*100\)

Or, \(ROI\) = \(20\) %

Thus, the answer must be (D) 20 %



Hi Abhishek009
Please explain the formula in detail.
Thanks in advance .
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Re: The compound interest on a certain sum of money invested at a certain [#permalink]

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New post 02 Jul 2017, 09:04
arvind910619 wrote:
Hi Abhishek009
Please explain the formula in detail.
Thanks in advance .


Dear arvind910619

There is no formula , its the basic concept of Compound Interest which distinguishes Simple Interest from Compound Interest.

In compound Interest we calculate interest for the Interest amount as well, whereas in Simple Interest we calculate Interest only on the principal amount.


Example -

SI on a sum of 100 for 3 years @ 20% pa will be -

\(SI = \frac{100*3*20}{100} = 60\)

CI on a sum of 100 for 3 years @ 20% pa will be -

Interest for 1st Year is \(\frac{100*1*20}{100}\) = \(20\)
Interest for 2nd Year is \(20\) + \(\frac{20*1*20}{100}\) = \(24\)
Interest for 3rd Year is \(24\) + \(\frac{24*1*20}{100}\) = \(28.8\)

Here in this question we are given Amount after 3rd Year, which Includes the Principal amount of 2nd Year which is 600 & Interest for 1 year , ie 120...

Hope this helps..

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Re: The compound interest on a certain sum of money invested at a certain [#permalink]

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New post 07 Sep 2017, 04:34
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Another way (which will lead to the one already posted):

Let x be the initial investment and y the interest rate:

\(x(1+y)^2 = 600\)
\(x(1+y)^3 = 720\)

Thus:
\(x(1+y)^2 = 600\)
\(x(1+y)^2 * (1+y) = 720\)

\(600 (1+y) = 720\)

\(y = 0,2\)
-> *100 -> 20%

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Re: The compound interest on a certain sum of money invested at a certain   [#permalink] 07 Sep 2017, 04:34
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