GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 24 Jan 2020, 10:06

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 an investment in 6 years is $400

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
B
Joined: 03 Nov 2019
Posts: 54
CAT Tests
The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 09 Dec 2019, 10:06
1
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

48% (01:53) correct 52% (02:54) wrong based on 21 sessions

HideShow timer Statistics

The Compound Interest on an investment in 6 years is $400 and Compound Interest on the same investment in 12 years is $ 960. Find the initial investment
A) 1250
B) 1200
C) 1000
D) 1500
E) 1100
VP
VP
User avatar
V
Joined: 19 Oct 2018
Posts: 1294
Location: India
Premium Member
Re: The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 09 Dec 2019, 21:17
We're getting 960-800=$160 interest on 400$ in 6 years

\(560=400(1+r/100)^6\)

\((1+r/100)^6\)= \(\frac{560}{400}= 1.4\)

Let initial investment= P

\(P+400= P(1+r/100)^6\)

P+400= 1.4P

0.4P=400
P=1000


Ansh777 wrote:
The Compound Interest on an investment in 6 years is $400 and Compound Interest on the same investment in 12 years is $ 960. Find the initial investment
A) 1250
B) 1200
C) 1000
D) 1500
E) 1100
Senior Manager
Senior Manager
avatar
G
Joined: 16 Feb 2015
Posts: 264
Location: United States
Concentration: Finance, Operations
Schools: INSEAD, ISB
The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 09 Dec 2019, 22:52
[quote="nick1816"]We're getting 960-800 =$160 interest on 400$ in 6 years

\(560=400(1+r/100)^6\)

\((1+r/100)^6\)= \(\frac{560}{400}= 1.4\)

Let initial investment= P

\(P+400= P(1+r/100)^6\)

P+400= 1.4P

0.4P=400
P=1000
------------------------------------
Dear nick1816 ,
If Possible Pls explain properly. Many doubt creating mistake/wording are there in your Explanation.

960-400 =560 $
In 6 Years, Amount of 400$ as interest increased by 560$
n=6, A= 560, P= 400
A=P*(1+r/100)^n
560=400(1+r/100)^6
(1+r/100)^6=1.4.

As We Know for 1st 6years, A=P+C.I = 400+P
A=P*(1+r/100)^n
400+P = P*(1.4)
400+P=1.4P
P=400/0.4=1000

IMO-C

:please Please Give Kudos, If you find my explanation Good Enough :please
VP
VP
User avatar
V
Joined: 19 Oct 2018
Posts: 1294
Location: India
Premium Member
The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 09 Dec 2019, 23:07
rajatchopra1994 You missed the logic i guess.

On P investment, we 're getting 400 bucks interest in 6 years, so we'll get the same interest in the next 6 years. Total is 400+400=800 bucks.
Whatever extra we're getting is the interest on the interest of first 6 years.








rajatchopra1994 wrote:
nick1816 wrote:
We're getting 960-800 =$160 interest on 400$ in 6 years

\(560=400(1+r/100)^6\)

\((1+r/100)^6\)= \(\frac{560}{400}= 1.4\)

Let initial investment= P

\(P+400= P(1+r/100)^6\)

P+400= 1.4P

0.4P=400
P=1000
------------------------------------
Dear nick1816 ,
If Possible Pls explain properly. Many doubt creating mistake/wording are there in your Explanation.

960-400 =560 $
In 6 Years, Amount of 400$ as interest increased by 560$
n=6, A= 560, P= 400
A=P*(1+r/100)^n
560=400(1+r/100)^6
(1+r/100)^6=1.4.

As We Know for 1st 6years, A=P+C.I = 400+P
A=P*(1+r/100)^n
400+P = P*(1.4)
400+P=1.4P
P=400/0.4=1000

IMO-C

:please Please Give Kudos, If you find my explanation Good Enough :please
Senior Manager
Senior Manager
avatar
G
Joined: 16 Feb 2015
Posts: 264
Location: United States
Concentration: Finance, Operations
Schools: INSEAD, ISB
Re: The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 09 Dec 2019, 23:39
Dear nick1816 ,

I already understood the explanation.
For others, it will be confusing to understand. That's why I have mentioned it.
Hope you will get my Point.

Regards,
Rajat Chopra
VP
VP
User avatar
V
Joined: 19 Oct 2018
Posts: 1294
Location: India
Premium Member
Re: The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 09 Dec 2019, 23:52
rajatchopra1994 bro if someone will have a doubt, he/she can ask or can refer your solution lol. These kinda things happen because of time constraint; you can't write everything brother. I don't understand why you're even bothering about if you understood the solution. Anyways, i'm outta this thread.

rajatchopra1994 wrote:
Dear nick1816 ,

I already understood the explanation.
For others, it will be confusing to understand. That's why I have mentioned it.
Hope you will get my Point.

Regards,
Rajat Chopra
Senior Manager
Senior Manager
avatar
G
Joined: 16 Feb 2015
Posts: 264
Location: United States
Concentration: Finance, Operations
Schools: INSEAD, ISB
Re: The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 09 Dec 2019, 23:58
nick1816 wrote:
rajatchopra1994 bro if someone will have a doubt, he/she can ask or can refer your solution lol. These kinda things happen because of time constraint; you can't write everything brother. I don't understand why you're even bothering about if you understood the solution. Anyways, i'm outta this thread.

rajatchopra1994 wrote:
Dear nick1816 ,

I already understood the explanation.
For others, it will be confusing to understand. That's why I have mentioned it.
Hope you will get my Point.

Regards,
Rajat Chopra


nick1816,

I thought we explain every question properly for the other members of GMAT Club Community.
That is the only reason for posting explained answers. I think i misunderstood the purpose of explanation.
Same here bro, outta from this thread. Regards!!
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8336
The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 10 Dec 2019, 00:08
1
1
Ansh777 wrote:
The Compound Interest on an investment in 6 years is $400 and Compound Interest on the same investment in 12 years is $ 960. Find the initial investment
A) 1250
B) 1200
C) 1000
D) 1500
E) 1100



Another way..

What is compound interest --- \(P(1+\frac{r}{100})^t-P=I\)

The Compound Interest on an investment in 6 years is $400----- --
\(P(1+\frac{r}{100})^6-P=400........\)..
\(P(1+\frac{r}{100})^6=P+400\)......
\((1+\frac{r}{100})^6=\frac{P+400}{P}\)...(i)

Similarly, Compound Interest on the same investment in 12 years is $ 960--------
\(P(1+\frac{r}{100})^{12}-P=400........\)..
\(P((1+\frac{r}{100})^6)^2=P+960\)...Substitute (i) in it.
\(P(\frac{400+P}{P})^2=960+P.........(400+P)^2=P(960+P)...P=1000\)

C
_________________
Intern
Intern
avatar
B
Joined: 12 Sep 2019
Posts: 5
Re: The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 13 Dec 2019, 10:21
chetan2u, Can you please expand (400+p)^2 = P(960+p), for some reason my solution isn't the same as yours.

Thanks.
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8336
Re: The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 13 Dec 2019, 20:04
cabpri28 wrote:
chetan2u, Can you please expand (400+p)^2 = P(960+p), for some reason my solution isn't the same as yours.

Thanks.



(400+p)^2=p(960+p).....160000+800p+p^2=960p+p^2
160000=960p-800p=160p.....p=1000
_________________
Rice (Jones) School Moderator
User avatar
P
Joined: 18 Jun 2018
Posts: 329
Location: United States (AZ)
Concentration: Finance, Healthcare
GMAT 1: 600 Q44 V28
GPA: 3.36
CAT Tests
The Compound Interest on an investment in 6 years is $400  [#permalink]

Show Tags

New post 13 Dec 2019, 20:41
1
This took me a little over 3 mins, but here is my approach:

Let P be the original amount and r = rate
There 400 + P = P\((1+r)^{6}\) ==> P(\((1+r)^{6}\) - 1) = 400 ==> Let's call this eq 1
Similarly, P(\((1+r)^{12}\) - 1) = 960 ==> Let's call this eq 2
Let x = \((1+r)^{6}\) ==> eq 1: P(x - 1) = 400 and eq 2: P(\(x^{2}\) - 1) = 960
Divide eq 1 by eq 2 (to cancel out P and x - 1) ==> \(\frac{1}{x+1}\) = \(\frac{5}{12}\) ==> x = \(\frac{7}{5}\)
Therefore, using eq 1, P = \(\frac{400}{x - 1}\) ==> P = 400/\(\frac{2}{5}\) ==> P = $1,000 (the answer is C)
GMAT Club Bot
The Compound Interest on an investment in 6 years is $400   [#permalink] 13 Dec 2019, 20:41
Display posts from previous: Sort by

The Compound Interest on an investment in 6 years is $400

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





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