GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Nov 2019, 22:41

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59095
The compound interest on a certain sum of money invested at a certain  [#permalink]

Show Tags

New post 02 Jul 2017, 02:42
1
8
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:52) correct 33% (02:14) wrong based on 99 sessions

HideShow timer Statistics

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3308
Location: India
GPA: 3.12
The compound interest on a certain sum of money invested at a certain  [#permalink]

Show Tags

New post 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
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4832
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: The compound interest on a certain sum of money invested at a certain  [#permalink]

Show Tags

New post 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
VP
User avatar
D
Status: Learning
Joined: 20 Dec 2015
Posts: 1025
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE: Engineering (Manufacturing)
Reviews Badge
Re: The compound interest on a certain sum of money invested at a certain  [#permalink]

Show Tags

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 .
_________________
Please give kudos if you find my answers useful
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4832
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: The compound interest on a certain sum of money invested at a certain  [#permalink]

Show Tags

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..

_________________
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 )
Intern
Intern
avatar
B
Joined: 21 Sep 2016
Posts: 28
Re: The compound interest on a certain sum of money invested at a certain  [#permalink]

Show Tags

New post 07 Sep 2017, 04:34
2
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%
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3308
Location: India
GPA: 3.12
The compound interest on a certain sum of money invested at a certain  [#permalink]

Show Tags

New post 02 Oct 2018, 00:01
1
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)
_________________
You've got what it takes, but it will take everything you've got
Manager
Manager
avatar
G
Joined: 11 Mar 2018
Posts: 150
CAT Tests
The compound interest on a certain sum of money invested at a certain  [#permalink]

Show Tags

New post 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
Manager
avatar
S
Joined: 10 Dec 2017
Posts: 132
Location: India
CAT Tests
Re: The compound interest on a certain sum of money invested at a certain  [#permalink]

Show Tags

New post 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
GMAT Club Bot
Re: The compound interest on a certain sum of money invested at a certain   [#permalink] 26 Oct 2019, 06:51
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne