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

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Math Expert
Joined: 02 Sep 2009
Posts: 47086
The compound interest on a certain sum of money invested at a certain [#permalink]

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02 Jul 2017, 02:42
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Difficulty:

35% (medium)

Question Stats:

71% (01:55) correct 29% (01:49) wrong based on 66 sessions

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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%

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

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02 Jul 2017, 02:52
1
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) _________________ You've got what it takes, but it will take everything you've got Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 3647 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: The compound interest on a certain sum of money invested at a certain [#permalink] ### Show Tags 02 Jul 2017, 03:06 1 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 % _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) VP Status: Learning Joined: 20 Dec 2015 Posts: 1206 Location: India Concentration: Operations, Marketing GMAT 1: 670 Q48 V36 GRE 1: Q157 V157 GPA: 3.4 WE: Manufacturing and Production (Manufacturing) Re: The compound interest on a certain sum of money invested at a certain [#permalink] ### Show Tags 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.
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Re: The compound interest on a certain sum of money invested at a certain [#permalink]

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

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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Thanks and Regards

Abhishek....

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Posts: 29
Re: The compound interest on a certain sum of money invested at a certain [#permalink]

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07 Sep 2017, 04:34
1

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