Last visit was: 14 Dec 2024, 22:33 It is currently 14 Dec 2024, 22:33
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Dec 2024
Posts: 97,877
Own Kudos:
685,932
 []
Given Kudos: 88,271
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,877
Kudos: 685,932
 []
The difference, after two years, between compound interest and simple 02 Jul 2017, 02:24
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

66% (02:22) correct 34% (02:51) wrong based on 157 sessions

History

Date
Time
Result
Not Attempted Yet
The difference, after two years, between compound interest and simple interest on a certain sum of money invested at the same rate of interest, is $18. If the simple interest accumulated on the sum after two years is $180, what is the rate of interest at which the sum of money was invested?

(A) 36%
(B) 30%
(C) 25%
(D) 20%
(E) 10%
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 24 Apr 2024
Posts: 2,856
Own Kudos:
5,588
 []
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,856
Kudos: 5,588
 []
The difference, after two years, between compound interest and simple 02 Jul 2017, 02:44
3
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
Given data : Compound Interest - Simple Interest(on the same sum of money) = 18$
Also, the period of interest : 2 yrs
Simple interest accumulated over 2 years = 180$

We know that the simple interest = compound interest(for the first year, for any amount for same rate of interest)
So, the difference in interests would have occurred in the second year.
Simple interest is going to be same for all years for any sum at
a fixed rate of interest(making the simple interest of year 1 = 90$)
Since the compound interest increases by 18$, the rate of interest must be 20%(because 20% of 90 is 18)

Hence, rate of interest : 20%(Option D)
General Discussion
avatar
roadrunner
avatar
Current Student
Joined: 23 Jul 2015
Last visit: 05 Sep 2023
Posts: 125
Own Kudos:
132
 []
Given Kudos: 31
Posts: 125
Kudos: 132
 []
The difference, after two years, between compound interest and simple 02 Jul 2017, 06:49
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
In compounding interest, interest earned in year t0 is reinvested for year t1 i.e. interest is earned on interest payments. In simple interest, fixed interest is paid each year (no interest on last year's payment)

==> simple interest each year = 180/2 = 90$

As total period is 2 years only, difference between compounding interest payment and simple interest payment arises from the interest earned on 1st year interest under CI.

ROI = 18/90 = 1/5 = 20%

Ans. is D
User avatar
ydmuley
User avatar
Retired Moderator
Joined: 19 Mar 2014
Last visit: 01 Dec 2019
Posts: 814
Own Kudos:
1,007
 []
Given Kudos: 199
Location: India
Concentration: Finance, Entrepreneurship
Schools: Haas '20 HBS '20 CBS '20 Wharton '20 Stanford '20 Kellogg '20
GPA: 3.5
Schools: Haas '20 HBS '20 CBS '20 Wharton '20 Stanford '20 Kellogg '20
Posts: 814
Kudos: 1,007
 []
The difference, after two years, between compound interest and simple 03 Jul 2017, 13:04
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
This is a very good question. Thanks Bunuel At least I am able to brush up the concepts for SI and CI. :)

Simple Interest For First Year = Compound Interest For the First Year

Simple Interest for 2 Years \(= $ 180\)

Simple Interest Per Year \(= $\frac{180}{2}\) \(= $90\)

Considering the difference between the Compound interest and Simple Interest for the second year \(= $18\)

We know that the compound interest add \($18\) in the \($90\)amount of the first year. This can give us the interest rate

\(= \frac{18}{90} = \frac{6}{30}= \frac{1}{5} = 20%\)


Hence, Anwer is D
avatar
anuj11
avatar
Joined: 19 Jan 2016
Last visit: 21 Apr 2018
Posts: 29
Own Kudos:
3
Given Kudos: 10
Posts: 29
Kudos: 3
The difference, after two years, between compound interest and simple 08 Jul 2017, 01:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi..

can someone explain why are we doing (18/90) ?? As 90 is the simple interest and 18 is the difference between the two interests ??
User avatar
TimeTraveller
User avatar
Joined: 28 Jun 2015
Last visit: 29 Jul 2017
Posts: 245
Own Kudos:
310
 []
Given Kudos: 47
Concentration: Finance
GPA: 3.5
Posts: 245
Kudos: 310
 []
The difference, after two years, between compound interest and simple 08 Jul 2017, 04:27
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
SI for 1st year = CI for 1st year = \($90\).

Let CI for the 2nd year = \(x\).

So, \(x - 90 = 18\)

\(x = $108\).

\(90 + 20\%(90) = 108\), so Ans - D.
avatar
sarugiri
avatar
Joined: 22 Oct 2016
Last visit: 30 Oct 2017
Posts: 17
Own Kudos:
19
 []
Given Kudos: 23
Posts: 17
Kudos: 19
 []
The difference, after two years, between compound interest and simple 20 Jul 2017, 06:27
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
anuj11
Hi..

can someone explain why are we doing (18/90) ?? As 90 is the simple interest and 18 is the difference between the two interests ??

Hi Anuj11,

We know SI is 180$ for 2yrs, making it 90$ for each year.

The difference b/w Simple and Compound interest starts from 2nd year.

Hence the interest amount of 2nd year[90$] is compounding, and the difference b/w SI and CI as per the stem is 18$. The question is asking 18$ difference is what % of the interest amount.

18 = (x/100)90
x = (1/5) = 20%

Hope it answers your doubt.
User avatar
DavidTutorexamPAL
User avatar
examPAL Representative
Joined: 07 Dec 2017
Last visit: 09 Sep 2020
Posts: 1,048
Own Kudos:
1,867
 []
Given Kudos: 26
Posts: 1,048
Kudos: 1,867
 []
The difference, after two years, between compound interest and simple 27 Sep 2018, 12:32
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The difference, after two years, between compound interest and simple interest on a certain sum of money invested at the same rate of interest, is $18. If the simple interest accumulated on the sum after two years is $180, what is the rate of interest at which the sum of money was invested?

(A) 36%
(B) 30%
(C) 25%
(D) 20%
(E) 10%

We'll use the underlying logic behind interest to create a simple equation, without bothering with variables.
This is a Logical approach.

The only difference between the compound and simple interest is that the compound interest was calculated twice - once at the end of the first year and once at the end of the second year.
So, the $18 difference must be due to the second year's interest earned from the first year's interest.
Since 2 years of simple interest is $180, one year is $90 so 90*rate = 18 meaning that our interest rate is 18/90 = 2/10 = 20%

(D) is our answer.

Note that understanding the underlying logic created an extremely simple calculation: 18 divided by (180/2), as opposed to something full of variables.
User avatar
US09
User avatar
Joined: 15 Oct 2017
Last visit: 06 Apr 2021
Posts: 248
Own Kudos:
267
 []
Given Kudos: 338
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Products:
My Reviews
GMAT 3: 710 Q49 V39
Posts: 248
Kudos: 267
 []
The difference, after two years, between compound interest and simple 28 Sep 2018, 04:53
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If simple interest was 180$, that means simple interest must have been 90$ per year. So, the difference in 18$ must have ocurred due to the interest in interest, i.e. (90*x)/100 = 18, x = 20%.

IMO D.
avatar
vipulshahi
avatar
Joined: 24 Sep 2013
Last visit: 30 Aug 2021
Posts: 164
Own Kudos:
111
Given Kudos: 40
Location: Saudi Arabia
GPA: 3.8
WE:Project Management (Energy)
Posts: 164
Kudos: 111
The difference, after two years, between compound interest and simple 30 Sep 2018, 11:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
urvashis09

Can you please elaborate the explaination which you mentioned above.

I have on concern , $18 is for 2 year , how you can take $90*x/100 = $18
User avatar
US09
User avatar
Joined: 15 Oct 2017
Last visit: 06 Apr 2021
Posts: 248
Own Kudos:
267
Given Kudos: 338
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Products:
My Reviews
GMAT 3: 710 Q49 V39
Posts: 248
Kudos: 267
The difference, after two years, between compound interest and simple 30 Sep 2018, 22:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
vipulshahi
urvashis09

Can you please elaborate the explaination which you mentioned above.

I have on concern , $18 is for 2 year , how you can take $90*x/100 = $18

Sure, when you calculate simple interest and compound interest for any given amount, the interest for the first year remains the same. Example, you have 100$ on both SI and CI for 2 years @ 10%, for the first year both will earn an interest of 10$. But for the second year, SI will again earn 10$, but CI will earn 11$. Why? because now the amount for CI becomes the amount initially invested plus the interest earned i.e. 100$ + 10$ = 110$. Since the interest earned is not taken out but added in the principal amount invested for CI, the difference starts coming from second year onwards.

Hope that helps.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 13 Dec 2024
Posts: 19,869
Own Kudos:
24,296
Given Kudos: 288
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 19,869
Kudos: 24,296
The difference, after two years, between compound interest and simple 09 Nov 2018, 13:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The difference, after two years, between compound interest and simple interest on a certain sum of money invested at the same rate of interest, is $18. If the simple interest accumulated on the sum after two years is $180, what is the rate of interest at which the sum of money was invested?

(A) 36%
(B) 30%
(C) 25%
(D) 20%
(E) 10%

Let’s let P = the principal and r = the interest rate., We use the formula for simple interest: I = P x r x t and the compound interest formula (for annual compounding): I = P x [(1 + r)^t -1], and we have:

P x r x 2 = 180 (from the simple interest formula)

P x [(1 + r)^2 - 1] = 198 (from the compound interest formula for annual compounding

Dividing the first equation by the second equation, we have:

(r x 2)/[(1 + r)^2 - 1]= 180/198

198(r x 2) = 180[(1 + r)^2 - 1]

198(2r) = 180(1 + 2r + r^2 - 1)

396r = 360r + 180r^2

180r^2 - 36r = 0

36r(5r - 1) = 0

r = 0

or

5r - 1 = 0

r = 1/5

Since r can’t be 0, r = 1/5 = 20%.

Answer: D
avatar
Elleo
avatar
Joined: 08 Mar 2018
Last visit: 12 Jun 2019
Posts: 1
Given Kudos: 3
Posts: 1
Kudos: 0
The difference, after two years, between compound interest and simple 10 Jun 2019, 10:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello,
Could you someone explain why above question doesn't mentioned the total amount of compound interest for 2 years?

If simple interest 90$ =compound interest 90$ .
It means 90+90=180 for first year.
If compound interest 108(90$x/100%=18$; 18+90)=90 simple interest.
It means 90+108=198 for the second year.

So totall sum of interest,as I understand, shall be 180+198= 378$ for two years.
Or did I miss something?

Posted from my mobile device
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,710
Own Kudos:
1,394
Given Kudos: 607
Location: United States
Posts: 1,710
Kudos: 1,394
The difference, after two years, between compound interest and simple 06 Nov 2019, 06:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The difference, after two years, between compound interest and simple interest on a certain sum of money invested at the same rate of interest, is $18. If the simple interest accumulated on the sum after two years is $180, what is the rate of interest at which the sum of money was invested?

(A) 36%
(B) 30%
(C) 25%
(D) 20%
(E) 10%

\(ar2=180…ar=90\)
\((a(1+r)^2-a)-ar2=18\)
\([ar+r(a+ar)]-ar2=18…[ar+ar+ar^2]-ar2=18…ar^2=18\)
\(ar=90…ar^2=18…90/r=18/r^2…90r^2=18r…r=18/90=1/5=0.2\)

Ans. (D)
Moderator:
Bunuel
Math Expert
97877 posts