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

It is currently 20 Sep 2018, 15:51

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

Donald plans to invest x dollars in a savings account that

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

Hide Tags

Manager
Manager
User avatar
Joined: 29 May 2008
Posts: 110
Donald plans to invest x dollars in a savings account that  [#permalink]

Show Tags

New post Updated on: 07 Jul 2013, 01:20
3
26
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (01:34) correct 31% (01:44) wrong based on 866 sessions

HideShow timer Statistics

Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A. 1500
B. 1750
C. 2000
D. 2500
E. 3000

Originally posted by TheRob on 19 Aug 2009, 06:44.
Last edited by Bunuel on 07 Jul 2013, 01:20, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49271
Re: Compounded Interest  [#permalink]

Show Tags

New post 07 Jul 2013, 01:37
7
6
nikhil007 wrote:
what wrong am I doing, can someone point out?

{x(1+.02)^2 } -x > 100

taking x common on LHS
(x)(1.02)^2 -1>100

(x)(1.02)^2 >101

(x) 1.04 >101

x= 101\1.04

I think i am doing some silly calculation mistake here, can someone point me out pl.


Algebra:
\(x(1+0.02)^2 -x > 100\)
\(x(1.02^2-1)>100\)
\(x*0.0404>100\)
\(x>\frac{100}{0.0404}\approx{2475.25}\)

Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
A. 1500
B. 1750
C. 2000
D. 2500
E. 3000

Annual rate of 8% compounded quarterly is approximately 4% in 6 months (a bit more).

x*0.04=100 --> x=2500.

Answer: D.

Similar questions to practice:
john-deposited-10-000-to-open-a-new-savings-account-that-135825.html
on-the-first-of-the-year-james-invested-x-dollars-at-128825.html
marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html
jolene-entered-an-18-month-investment-contract-that-127308.html
alex-deposited-x-dollars-into-a-new-account-126459.html
michelle-deposited-a-certain-sum-of-money-in-a-savings-138273.html
leona-bought-a-1-year-10-000-certificate-of-deposit-that-143742.html

Theory:
math-number-theory-percents-91708.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Manager
Manager
User avatar
Joined: 18 Feb 2010
Posts: 160
Schools: ISB
Re: Compounded Interest  [#permalink]

Show Tags

New post 07 Mar 2010, 00:27
12
9
TheRob wrote:
Sorry i posted a rate problem with the wrong title
Here you have the real problem of comound interest, I kind of have the idea but I don not know how to apply the formula

Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

$1500
$1750
$2000
$2500
$3000




Lets solve it under 30 seconds...

8% compounded quarterly = 2% per quarter = 4% for half year

if 4% is 100 then 100% would be 2500.....Answer D. What say....

Hope this works !!!
_________________

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!

General Discussion
Manager
Manager
avatar
Joined: 17 Dec 2007
Posts: 96
Re: Compounded Interest  [#permalink]

Show Tags

New post 19 Aug 2009, 09:18
2
TheRob wrote:
Sorry i posted a rate problem with the wrong title
Here you have the real problem of comound interest, I kind of have the idea but I don not know how to apply the formula

Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

$1500
$1750
$2000
$2500
$3000


Compound interest formula

A = P ( 1+r/n)power nt

given, n= 4 (quaterly);r =.08

the approach is substitution,

our interest requirement is 100$ after 6 months, 2 compounding period. interest per compounding period is 2%

lets take 1500, after 3 months interest accumulated is 30$, total amount is 1530
after 6 months, interest is 30.6$ and total is 1560.6$, so not 1500

1500 & 1750 have a difference of 250$ only , but the expected interest different is around 40$ hence you can straightaway rule out 1750

2000 is again can be ruled out as approx 4% interest yeilds only 80$

2500$ is a good bet, first 3 months it earns 50$ as interest, next 3 months it will earn 51$ as interest.
hence answer is D
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 813
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Compounded Interest  [#permalink]

Show Tags

New post 19 Aug 2009, 10:34
5
4
E.

For CI:
Final amount = Principal(1+ r/n)^nt
Let principal = x, then final amount = x+100

x+100 = x[1+ 0.02]^2
x+100 = 1.04x
0.04x=100
x=2500

so if 2500 is invested CI will be exactly 100. To earn more interest more principal should be invested. So E.
Manager
Manager
User avatar
Joined: 29 May 2008
Posts: 110
Re: Compounded Interest  [#permalink]

Show Tags

New post 19 Aug 2009, 11:57
1
Thank you veyr much here is the book explanation

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years
In this case, x represents the unknown principal, r = 8%, n = 4 since the compounding is done quarterly, and t = .5 since the time frame in question is half a year (6 months).
You can solve this problem without using compound interest. 8% interest over half a year, however that interest is compounded, is approximately 4% interest. So, to compute the principal, it's actually a very simple calculation:
100 = .04x
2500 = x
The correct answer is D.
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 813
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Compounded Interest  [#permalink]

Show Tags

New post 19 Aug 2009, 22:20
1
Unfortunately I dont agree with the OE if I am understanding the question correctly.

If we invest 2500, then CI will ONLY be 100.
Question asks "to earn over $100" how much amount is to be invested. Considering rate of interest, number of years and everything else to be the same, the only way to earn CI>100 is to increase the Principal Amount because CI is directly proportional to Principal Amount.

On test day I would have chosen E for sure. What is the source though?
Intern
Intern
avatar
Joined: 09 Aug 2009
Posts: 46
Re: Compounded Interest  [#permalink]

Show Tags

New post 19 Aug 2009, 23:14
1
Economist wrote:
Unfortunately I dont agree with the OE if I am understanding the question correctly.

If we invest 2500, then CI will ONLY be 100.
Question asks "to earn over $100" how much amount is to be invested. Considering rate of interest, number of years and everything else to be the same, the only way to earn CI>100 is to increase the Principal Amount because CI is directly proportional to Principal Amount.

On test day I would have chosen E for sure. What is the source though?


For P=2500, first 3 months you earn 50$ as interest, next 3 months it will earn 51$ as interest. So total 101$. I guess D should be fine
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 813
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Compounded Interest  [#permalink]

Show Tags

New post 19 Aug 2009, 23:47
Economist wrote:
E.

For CI:
Final amount = Principal(1+ r/n)^nt
Let principal = x, then final amount = x+100

x+100 = x[1+ 0.02]^2
x+100 = 1.04x
0.04x=100
x=2500

so if 2500 is invested CI will be exactly 100. To earn more interest more principal should be invested. So E.


OK. I got the problem, the reason is that I rounded off 1.02^2 in the above calculation. Precisely it is 1.0404 and then we get x= 2475. So anything >2475 will give CI >100 :)
The .xx04 made the difference :) Hence, either I should be very precise and not round off for CI problems or solve via back tracking.
Senior Manager
Senior Manager
avatar
Joined: 07 Nov 2009
Posts: 262
Donald plans to invest x dollars in a savings account that pays intere  [#permalink]

Show Tags

New post 21 Jul 2010, 22:34
4
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

A. $1500
B. $1750
C. $2000
D. $2500
E. $3000

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years
Manager
Manager
avatar
Joined: 20 Jul 2010
Posts: 138
Re: Donald plans to invest x dollars in a savings account that pays intere  [#permalink]

Show Tags

New post 22 Jul 2010, 00:06
1
2
IMO D
rohitgoel15 wrote:
Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
$1500
$1750
$2000
$2500
$3000

The formula for calculating compound interest is A = P(1 + r/n)nt where the variables represent the following:
A = amount of money accumulated after t years (principal + interest)
P = principal investment
r = interest rate (annual)
n = number of times per year interest is compounded
t = number of years


Solution:
r = Rate = 8% compounded quarterly.. = 2% per quarter
t = 6 motnhs = 2 quarters
So A = P (1+0.02)^2
=> A = P * 1.0404

Subsitute, P for 1500, 1700, 2000.. The A-P should be greater than 100 (since Interest = Amount - principal).
For 2500, interest is 101...

Hence, D
_________________

Gotta hit the 700 score this time... 3rd time lucky !
Give me some kudos... Like you, even I need them badly ;)

CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2617
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: Donald plans to invest x dollars in a savings account that pays intere  [#permalink]

Show Tags

New post 22 Jul 2010, 00:20
3
1
A = P(1 + r/n)nt here t =1/2 and n=4
=> A = P(1 + 8 %/4)4*(1/2)
=> A = P(1 + 2%)^2
=> A = P ( 1+ (2%)^2 + 4%) ,(2%)^2 is very small and can be ignored

=> A = P ( 1+4%) => A-P = P*4%
Also A-P = 100 => P = 100/4% = 100*100/4 = 2500
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Manager
Manager
avatar
Joined: 04 Dec 2011
Posts: 67
Schools: Smith '16 (I)
GMAT ToolKit User
Re: Compounded Interest  [#permalink]

Show Tags

New post 07 Jul 2013, 00:21
what wrong am I doing, can someone point out?

{x(1+.02)^2 } -x > 100

taking x common on LHS
(x)(1.02)^2 -1>100

(x)(1.02)^2 >101

(x) 1.04 >101

x= 101\1.04

I think i am doing some silly calculation mistake here, can someone point me out pl.
_________________

Life is very similar to a boxing ring.
Defeat is not final when you fall down…
It is final when you refuse to get up and fight back!

1 Kudos = 1 thanks
Nikhil

Intern
Intern
avatar
Joined: 01 Jul 2013
Posts: 2
Location: United States
Concentration: General Management, Strategy
Schools: Insead '14, ISB '15
GPA: 4
WE: Business Development (Computer Software)
Re: Compounded Interest  [#permalink]

Show Tags

New post Updated on: 07 Jul 2013, 04:19
nikhil007 wrote:
what wrong am I doing, can someone point out?

{x(1+.02)^2 } -x > 100

taking x common on LHS
(x)(1.02)^2 -1>100

(x)(1.02)^2 >101

(x) 1.04 >101

x= 101\1.04

I think i am doing some silly calculation mistake here, can someone point me out pl.
:roll:


Hi Nikhil,

why don't use the simple formula:

CI = P(R/N)^NT

P= x
CI = 100
N= 4
T = 1/2 = 0.5

=> P = 100/ (.08/4)^(4*0.5)
=> P = 100/ (.02)^2
=> p = 100/ (4 * 10^-4)
=> P = 10^6/4
=> P = 25,000

;)

Originally posted by arunraj on 07 Jul 2013, 01:26.
Last edited by arunraj on 07 Jul 2013, 04:19, edited 1 time in total.
Manager
Manager
avatar
Joined: 04 Dec 2011
Posts: 67
Schools: Smith '16 (I)
GMAT ToolKit User
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

Show Tags

New post 07 Jul 2013, 03:33
1
Damn..when will I stop making these silly mistakes.. :(
_________________

Life is very similar to a boxing ring.
Defeat is not final when you fall down…
It is final when you refuse to get up and fight back!

1 Kudos = 1 thanks
Nikhil

Senior Manager
Senior Manager
User avatar
Joined: 03 Dec 2012
Posts: 256
Re: Compounded Interest  [#permalink]

Show Tags

New post 28 Nov 2013, 02:35
arunraj wrote:
nikhil007 wrote:
what wrong am I doing, can someone point out?

{x(1+.02)^2 } -x > 100

taking x common on LHS
(x)(1.02)^2 -1>100

(x)(1.02)^2 >101

(x) 1.04 >101

x= 101\1.04

I think i am doing some silly calculation mistake here, can someone point me out pl.
:roll:


Hi Nikhil,

why don't use the simple formula:

CI = P(R/N)^NT

P= x
CI = 100
N= 4
T = 1/2 = 0.5

=> P = 100/ (.08/4)^(4*0.5)
=> P = 100/ (.02)^2
=> p = 100/ (4 * 10^-4)
=> P = 10^6/4
=> P = 25,000

;)



I think you have quoted the incorrect formula for CI.
Intern
Intern
avatar
Joined: 08 Jul 2013
Posts: 19
GMAT ToolKit User
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

Show Tags

New post 13 Nov 2014, 06:43
Hi Bunnel,

Would it be correct to do the following.

I used the simple interest formula.
Since CI will give a greater amount than SI. an the interest is compounded quaterly. The rate for a quater would be 2%
Since the duration is 6 months there would be two compounding periods. $50 per period.

so... 50= (X. 2.1)/ 100

X would be 2500.... This is SI so CI would be obviously greater.

IS this method correct.?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49271
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

Show Tags

New post 13 Nov 2014, 06:48
vivekvijayan wrote:
Hi Bunnel,

Would it be correct to do the following.

I used the simple interest formula.
Since CI will give a greater amount than SI. an the interest is compounded quaterly. The rate for a quater would be 2%
Since the duration is 6 months there would be two compounding periods. $50 per period.

so... 50= (X. 2.1)/ 100

X would be 2500.... This is SI so CI would be obviously greater.

IS this method correct.?


Yes, 50= x*0.02 is correct.

Check other Compound Interest Problems in our Special Questions Directory.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1834
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

Show Tags

New post 13 Nov 2014, 23:40
2
Answer = D = 2500

For small amount, small duration (in 6 months), with quarterly compounding, there would be hardly major difference between SI & CI.

We can safely use the SI formula after proper adjustments

SI = 100

Principal = p (Required to be calculated)

RoI = 8% PA = 4% for 6 months

\(100 = p * \frac{4}{100}\)

\(p = \frac{100*100}{4} = 2500\)
_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
avatar
Joined: 28 Dec 2013
Posts: 68
Re: Donald plans to invest x dollars in a savings account that  [#permalink]

Show Tags

New post 30 Jan 2016, 12:45
mustdoit wrote:
TheRob wrote:
Sorry i posted a rate problem with the wrong title
Here you have the real problem of comound interest, I kind of have the idea but I don not know how to apply the formula

Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

$1500
$1750
$2000
$2500
$3000




Lets solve it under 30 seconds...

8% compounded quarterly = 2% per quarter = 4% for half year

if 4% is 100 then 100% would be 2500.....Answer D. What say....

Hope this works !!!

if 4% is 100 then 100% would be 2500 -->> how did you get to 2500 exactly
Re: Donald plans to invest x dollars in a savings account that &nbs [#permalink] 30 Jan 2016, 12:45

Go to page    1   2    Next  [ 28 posts ] 

Display posts from previous: Sort by

Donald plans to invest x dollars in a savings account that

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.