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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
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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, 02:42
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Question Stats:

67% (01:52) correct 33% (02:14) wrong based on 99 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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07 Sep 2017, 04:34
2

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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02 Jul 2017, 03:06
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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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02 Oct 2018, 00:01
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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%

Concept tested
The difference in the compound interests between any two consecutive years includes additional interest,
which is nothing but the interest calculated on the compound interest earned in the first of the consecutive
years.

In this problem, the compound interest for the amount is $600 for the second year & the interest calculated for the third year is$720. The difference in interest is $120, which is the interest earned on$600. We can
calculate the rate of interest as follows - $$\frac{120}{600} * 100 = 20%$$

Therefore, the rate of interest on which the amount was invested is 20%(Option D)
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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 VP Status: Learning Joined: 20 Dec 2015 Posts: 1027 Location: India Concentration: Operations, Marketing GMAT 1: 670 Q48 V36 GRE 1: Q157 V157 GPA: 3.4 WE: Engineering (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. Thanks in advance . _________________ Please give kudos if you find my answers useful Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4835 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, 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.. _________________ 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 ) Manager Joined: 11 Mar 2018 Posts: 155 The compound interest on a certain sum of money invested at a certain [#permalink] ### Show Tags Updated on: 26 Oct 2019, 18:23 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% Let x be the principal amount Let y be the rate of interest. We also know $$Compound Interest = Principal [1 +\frac{R}{100}]^N - Principal$$ Now using the same formula and details as per the question we get, $$600 = x[1 + \frac{y}{100}]^2 - x$$ --- (1) $$720 = x[1 + \frac{y}{100}]^3 - x$$ --- (2) Subtracting (1) from (2), we get $$120 = x[1 + \frac{y}{100}]^3 - x[1 + \frac{y}{100}]^2$$ $$120 = x[1 + \frac{y}{100}]^2 (1 + \frac{y}{100} - 1)$$ $$120 = x[1 + \frac{y}{100}]^2 (\frac{y}{100})$$ --- (3) Using (1) in (3), we get $$120 = 600 (\frac{y}{100})$$ $$\frac{1}{5} = \frac{y}{100}$$ y = 20 Hence D _________________ Regards AD --------------------------------- A Kudos is one more question and its answer understood by somebody !!! Originally posted by adstudy on 26 Oct 2019, 05:17. Last edited by adstudy on 26 Oct 2019, 18:23, edited 1 time in total. Manager Joined: 10 Dec 2017 Posts: 132 Location: India Re: The compound interest on a certain sum of money invested at a certain [#permalink] ### Show Tags 26 Oct 2019, 06:51 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%

Let the interest rate is X
{(1+X/100)^3}/{(1+X/100)^2}=720/600
1+X/100=6/5
X=20
D:)
How to get the equations
Principle amount is P and interest is X, after one year principle amount becomes P1
P1=P+P*X/100
P1=P(1+X/100)
P2=P1+P1*X/100
P2=P1(1+X/100)
P2=P(1+X/100)^2
P3=P(1+X/100)^3
(1+X/100)^3 is nothing but interest after 3 years that is 720 in this problem
same way (1+X/100)^2 interest after 2 years-620
Re: The compound interest on a certain sum of money invested at a certain   [#permalink] 26 Oct 2019, 06:51
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