NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 09:38 It is currently 25 Apr 2024, 09:38
Decision Tracker
My Rewards
New posts
New comers' posts

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

A college student expects to earn at least $1,000 in interest on an in

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
HarveyKlaus
Manager
Manager
Joined: 18 Feb 2015
Posts: 71
Own Kudos [?]: 567 [7]
Given Kudos: 15
Send PM
A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   20 Aug 2016, 04:18
1
Kudos
6
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

50% (01:50) correct 50% (02:50) wrong based on 98 sessions
Hide Show timer Statistics
A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

A) 4.91
B) 4.21
C) 5.72
D) 3.14
E) 1.08
ShowHide Answer
Official Answer
A
User avatar
Senthil1981
Manager
Manager
Joined: 23 Apr 2015
Posts: 234
Own Kudos [?]: 510 [2]
Given Kudos: 36
Location: United States
Concentration: General Management, International Business
Schools: Booth PT '19 Ross Weekend"19
WE:Engineering (Consulting)
Send PM
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   20 Aug 2016, 13:04
1
Bookmarks
HarveyKlaus wrote:
A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

A) 4.91
B) 4.21
C) 5.72
D) 3.14
E) 1.08




Formula for Total if compounded quarterly is =\(P ( 1+ r/4 ) ^4\) for one year. Where r is in %.
So here, \(21,000 = 20,000 (1 + r/4)^4\)
= \(21/20 = 1.05 = (1 + r/4)^4\)
Then pick the median value from the choice (4.21 here) and substitute for r , make sure to convert from %
\((1+4.21/400)^4 < 1.05\)

If \(r = 4.91, (1+4.91/400)^4 = 1.05\). So 4.91 will give the minimum value for rate.
Answer is A







+1 for kudos
User avatar
L
abhimahna
Board of Directors
Joined: 18 Jul 2015
Status:Emory Goizueta Alum
Posts: 3600
Own Kudos [?]: 5425 [0]
Given Kudos: 346
Send PM
Reviews Badge
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   21 Aug 2016, 01:11
Expert Reply
Senthil1981 wrote:
HarveyKlaus wrote:
A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

A) 4.91
B) 4.21
C) 5.72
D) 3.14
E) 1.08




Formula for Total if compounded quarterly is =\(P ( 1+ r/4 ) ^4\) for one year. Where r is in %.
So here, \(21,000 = 20,000 (1 + r/4)^4\)
= \(21/20 = 1.05 = (1 + r/4)^4\)
Then pick the median value from the choice (4.21 here) and substitute for r , make sure to convert from %
\((1+4.21/400)^4 < 1.05\)

If \(r = 4.91, (1+4.91/400)^4 = 1.05\). So 4.91 will give the minimum value for rate.
Answer is A

+1 for kudos


Can you please help me understand how did you solve the abobe two highlighted equations? I want to know if there is any easy way to get the answer.
User avatar
Senthil1981
Manager
Manager
Joined: 23 Apr 2015
Posts: 234
Own Kudos [?]: 510 [0]
Given Kudos: 36
Location: United States
Concentration: General Management, International Business
Schools: Booth PT '19 Ross Weekend"19
WE:Engineering (Consulting)
Send PM
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   21 Aug 2016, 09:45
abhimahna wrote:
Can you please help me understand how did you solve the abobe two highlighted equations? I want to know if there is any easy way to get the answer.



Hi Abhimahna,

I used onscreen calculator for taking twice the square root of (\(\sqrt{1.05}\)) and then solve for \(r\). Not aware of another approach.
Share if you come across.




+1 for kudos
User avatar
L
abhimahna
Board of Directors
Joined: 18 Jul 2015
Status:Emory Goizueta Alum
Posts: 3600
Own Kudos [?]: 5425 [0]
Given Kudos: 346
Send PM
Reviews Badge
A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   21 Aug 2016, 09:57
Expert Reply
Senthil1981 wrote:
abhimahna wrote:
Can you please help me understand how did you solve the abobe two highlighted equations? I want to know if there is any easy way to get the answer.



Hi Abhimahna,

I used onscreen calculator for taking twice the square root of (\(\sqrt{1.05}\)) and then solve for \(r\). Not aware of another approach.
Share if you come across.




+1 for kudos


Sorry my friend. That is not the right approach to solve this question then.

Please note that this is a PS question and we are not going to get Onscreen calculator for the same. We need to ask/look for some other solution.

Experts, Please help!!
User avatar
Senthil1981
Manager
Manager
Joined: 23 Apr 2015
Posts: 234
Own Kudos [?]: 510 [0]
Given Kudos: 36
Location: United States
Concentration: General Management, International Business
Schools: Booth PT '19 Ross Weekend"19
WE:Engineering (Consulting)
Send PM
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   21 Aug 2016, 10:16
abhimahna wrote:

Sorry my friend. That is not the right approach to solve this question then.

Please note that this is a PS question and we are not going to get Onscreen calculator for the same. We need to ask/look for some other solution.

Experts, Please help!!



Thanks Abhimahna for pointing this. I'll look for another approach.
User avatar
Senthil1981
Manager
Manager
Joined: 23 Apr 2015
Posts: 234
Own Kudos [?]: 510 [0]
Given Kudos: 36
Location: United States
Concentration: General Management, International Business
Schools: Booth PT '19 Ross Weekend"19
WE:Engineering (Consulting)
Send PM
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   21 Aug 2016, 10:29
abhimahna wrote:
Can you please help me understand how did you solve the abobe two highlighted equations? I want to know if there is any easy way to get the answer.



I tried binomial theorem and applied to first power \((1 + x)^n = 1 + nx\) and it gave \(r\) as \(5%\) and closest to \(5%\) is \(4.91\).
User avatar
S
kannu44
Manager
Manager
Joined: 17 Aug 2012
Posts: 88
Own Kudos [?]: 67 [2]
Given Kudos: 143
Location: India
Concentration: General Management, Strategy
GPA: 3.75
WE:Consulting (Energy and Utilities)
Send PM
GMAT ToolKit User
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   26 Apr 2017, 01:30
2
Kudos
I used approximation here . For simple interest , 5 % rate willl give interest of 1000$ on 20000$ . When it is compounded interest rate will be marginally lower .
User avatar
Shrija786
Intern
Intern
Joined: 18 May 2018
Posts: 5
Own Kudos [?]: 2 [0]
Given Kudos: 2
Send PM
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   19 Oct 2018, 11:25
Senthil1981 wrote:
HarveyKlaus wrote:
A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

A) 4.91
B) 4.21
C) 5.72
D) 3.14
E) 1.08




Formula for Total if compounded quarterly is =\(P ( 1+ r/4 ) ^4\) for one year. Where r is in %.
So here, \(21,000 = 20,000 (1 + r/4)^4\)
= \(21/20 = 1.05 = (1 + r/4)^4\)
Then pick the median value from the choice (4.21 here) and substitute for r , make sure to convert from %
\((1+4.21/400)^4 < 1.05\)

If \(r = 4.91, (1+4.91/400)^4 = 1.05\). So 4.91 will give the minimum value for rate.
Answer is A







+1 for kudos



Can anybody please elucidate the problem again? Where did we get 21,000 from?
User avatar
G
pandeyashwin
Manager
Manager
Joined: 14 Jun 2018
Posts: 171
Own Kudos [?]: 257 [0]
Given Kudos: 176
Send PM
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   19 Oct 2018, 12:21
Shrija786 wrote:
Senthil1981 wrote:
HarveyKlaus wrote:
A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

A) 4.91
B) 4.21
C) 5.72
D) 3.14
E) 1.08




Formula for Total if compounded quarterly is =\(P ( 1+ r/4 ) ^4\) for one year. Where r is in %.
So here, \(21,000 = 20,000 (1 + r/4)^4\)
= \(21/20 = 1.05 = (1 + r/4)^4\)
Then pick the median value from the choice (4.21 here) and substitute for r , make sure to convert from %
\((1+4.21/400)^4 < 1.05\)

If \(r = 4.91, (1+4.91/400)^4 = 1.05\). So 4.91 will give the minimum value for rate.
Answer is A







+1 for kudos



Can anybody please elucidate the problem again? Where did we get 21,000 from?

Amount = Principal + Interest
21000 = 20000 + 1000
User avatar
Shrija786
Intern
Intern
Joined: 18 May 2018
Posts: 5
Own Kudos [?]: 2 [0]
Given Kudos: 2
Send PM
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   19 Oct 2018, 12:23
Can you please also explain the inequality sign?
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5344
Own Kudos [?]: 3964 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   18 Aug 2019, 23:25
HarveyKlaus wrote:
A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?

A) 4.91
B) 4.21
C) 5.72
D) 3.14
E) 1.08


Given:
1. A college student expects to earn at least $1,000 in interest on an initial investment of $20,000.
2. The money is invested for one year at interest compounded quarterly.

Asked: What is the least annual interest rate that would achieve the goal?

A college student expects to earn at least $1,000 in interest on an initial investment of $20,000.
Interest rate expected = $1000/$20000 = 5% annually
Let the annual interest rate that would achieve the goal of 5% annual interest rate be x%

The money is invested for one year at interest compounded quarterly.
\((1 + x/4)^4 - 1 > 5%\)
\((1+x/4)^4>1.05\)
If x=4.91%
\((1+x/4)^4 = 1.05001>1.05\)

IMO A
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32674
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink] New post   08 Mar 2021, 11:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: A college student expects to earn at least $1,000 in interest on an in [#permalink]
08 Mar 2021, 11:03
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions