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

It is currently 17 Oct 2018, 10:12

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

If $20,000 were deposited into an account which yields x percent annua

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49968
If $20,000 were deposited into an account which yields x percent annua  [#permalink]

Show Tags

New post 14 Jan 2018, 06:50
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

54% (02:20) correct 46% (02:21) wrong based on 71 sessions

HideShow timer Statistics

If $20,000 were deposited into an account which yields x percent annual interest compounded quarterly the total value after 6 months was $20,808, what is the value of x?

A. 0.08
B. 2
C. 4
D. 8
E. 8.8

_________________

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

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3182
Location: India
GPA: 3.12
Premium Member CAT Tests
If $20,000 were deposited into an account which yields x percent annua  [#permalink]

Show Tags

New post 15 Jan 2018, 01:33
Bunuel wrote:
If $20,000 were deposited into an account which yields x percent annual interest compounded quarterly the total value after 6 months was $20,808, what is the value of x?

A. 0.08
B. 2
C. 4
D. 8
E. 8.8


Formula to calculate compound interest
(when compounded quarterly, rate = (\(\frac{x}{4}\)%) quarterly and time = (4n) quarter years)

Amount = Principal\((1+ \frac{x}{400})^{4n}\)

Here, we need to find the rate (x) at which the principal of 20000$ became 20808$
over a period of 6 months, n=\(\frac{1}{2}\)

\(20808 = 20000(1 + \frac{x}{400})^2\) => \(\frac{20808}{20000}= (1 + \frac{x}{400})^2\)

\((\frac{400 + x}{400})^2 = \frac{10404}{10000} = 1.0404\) => \(\frac{400 + x}{400} =\sqrt{1.0404} = 1.02\)

Solving for x, x = 8(Option D)
_________________

You've got what it takes, but it will take everything you've got

Senior Manager
Senior Manager
User avatar
V
Joined: 06 Jan 2015
Posts: 487
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Premium Member
Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

Show Tags

New post 15 Jan 2018, 02:07
pushpitkc wrote:
Bunuel wrote:
If $20,000 were deposited into an account which yields x percent annual interest compounded quarterly the total value after 6 months was $20,808, what is the value of x?

A. 0.08
B. 2
C. 4
D. 8
E. 8.8


Formula to calculate compound interest
(when compounded quarterly, rate = (\(\frac{x}{4}\)%) quarterly and time = (4n) quarter years)

Amount = Principal\((1+ \frac{x}{400})^{4n}\)

Here, we need to find the rate (x) at which the principal of 20000$ became 20808$
over a period of 6 months, n=\(\frac{1}{2}\)

\(20808 = 20000(1 + \frac{x}{400})^2\) => \(\frac{20808}{20000}= (1 + \frac{x}{400})^2\)

\((\frac{400 + x}{400})^2 = \frac{10404}{10000} = 1.0404\) => \(\frac{400 + x}{400} =\sqrt{1.0404} = 1.02\)

Solving for x, x = 8(Option D)


HI pushpitkc,

One quick que

Is it \(\frac{20808}{20000}= (1 + \frac{x}{400})^2\) should be \((1 + \frac{x}{200})^2\) Bcoz the total value after 6 months was $20,808 we are calculating or compounding twice.
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3182
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

Show Tags

New post 15 Jan 2018, 02:14
NandishSS wrote:
pushpitkc wrote:
Bunuel wrote:
If $20,000 were deposited into an account which yields x percent annual interest compounded quarterly the total value after 6 months was $20,808, what is the value of x?

A. 0.08
B. 2
C. 4
D. 8
E. 8.8


Formula to calculate compound interest
(when compounded quarterly, rate = (\(\frac{x}{4}\)%) quarterly and time = (4n) quarter years)

Amount = Principal\((1+ \frac{x}{400})^{4n}\)

Here, we need to find the rate (x) at which the principal of 20000$ became 20808$
over a period of 6 months, n=\(\frac{1}{2}\)

\(20808 = 20000(1 + \frac{x}{400})^2\) => \(\frac{20808}{20000}= (1 + \frac{x}{400})^2\)

\((\frac{400 + x}{400})^2 = \frac{10404}{10000} = 1.0404\) => \(\frac{400 + x}{400} =\sqrt{1.0404} = 1.02\)

Solving for x, x = 8(Option D)


HI pushpitkc,

One quick que

Is it \(\frac{20808}{20000}= (1 + \frac{x}{400})^2\) should be \((1 + \frac{x}{200})^2\) Bcoz the total value after 6 months was $20,808 we are calculating or compounding twice.


Hi NandishSS

Over the 6 months, the interest has been compounded twice(since interest in being calculated quarterly)

Also, the rate of interest is x for an entire year. The interest part quarterly must be \(\frac{x}{4}\)
The time period is 6 months, which comprises of 2 quarters. Hence, n=2

Hope this clears your confusion!
_________________

You've got what it takes, but it will take everything you've got

Senior Manager
Senior Manager
User avatar
P
Joined: 07 Dec 2017
Posts: 282
Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

Show Tags

New post 15 Jan 2018, 06:49
Answer is:D

We can directly solve it by simply substituting values from choices

Tip always switch between sparse variables



Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Intern
Intern
avatar
B
Joined: 06 Oct 2017
Posts: 17
Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

Show Tags

New post 18 Jan 2018, 11:29
1
Bunuel wrote:
If $20,000 were deposited into an account which yields x percent annual interest compounded quarterly the total value after 6 months was $20,808, what is the value of x?

A. 0.08
B. 2
C. 4
D. 8
E. 8.8





You essentially have to work backwards from a simple compound interest question. What helped me was looking at the answer choices and doing trial and error from there. But there might be a better option?

If x% compounds quarterly it compounds every 3 months, hence it will compound twice after 6 months. If we use answer choice D, 8%, it compounds 4 times a year so it will compound at one fourth of its total interest.

So there will be a 2% increase each year. So hypothetically, we'd have to do 102% of 102% of 20,000.

100% of 20,000 = 20,000
1% of 20,000 = 200
1% again = 200
so 102% of 20,000 = 20,400

now, 102% of 20,400 = 20,808

Hence, D is correct
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3845
Location: United States (CA)
Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

Show Tags

New post 21 Jan 2018, 20:01
1
Bunuel wrote:
If $20,000 were deposited into an account which yields x percent annual interest compounded quarterly the total value after 6 months was $20,808, what is the value of x?

A. 0.08
B. 2
C. 4
D. 8
E. 8.8


If the interest is compounded quarterly, the interest is compounded twice in 6 months. Using the compound interest formula,, we can set up the following equation (notice that x percent in the equation is expressed as x/100):

20,000(1 + (x/100)/4))^2 = 20808

(1 + x/400)^2 = 1.0404

Taking the square root of both sides, we have:

1 + x/400 = 1.02

x/400 = 0.02

x = 8

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Manager
User avatar
B
Joined: 26 Sep 2017
Posts: 96
Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

Show Tags

New post 23 Jan 2018, 08:37
ScottTargetTestPrep wrote:
Bunuel wrote:
If $20,000 were deposited into an account which yields x percent annual interest compounded quarterly the total value after 6 months was $20,808, what is the value of x?

A. 0.08
B. 2
C. 4
D. 8
E. 8.8


If the interest is compounded quarterly, the interest is compounded twice in 6 months. Using the compound interest formula,, we can set up the following equation (notice that x percent in the equation is expressed as x/100):

20,000(1 + (x/100)/4))^2 = 20808

(1 + x/400)^2 = 1.0404

Taking the square root of both sides, we have:

1 + x/400 = 1.02

x/400 = 0.02

x = 8

Answer: D

Hi scott

Here how to get sqrt 1.0404 without wasting time..?????

Sent from my BND-AL10 using GMAT Club Forum mobile app
Intern
Intern
avatar
B
Joined: 18 May 2017
Posts: 3
Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

Show Tags

New post 03 Feb 2018, 21:23
Bunuel wrote:
If $20,000 were deposited into an account which yields x percent annual interest compounded quarterly the total value after 6 months was $20,808, what is the value of x?

A. 0.08
B. 2
C. 4
D. 8
E. 8.8


we can even do it simply by calculating the simple interest i suppose.
20000*x/100*1/2=808
100x=808
x=8.08
Since the compound interest rate will be smaller than this rate,yet closer to it,i guess d will be the ans.
correct me if i'm wrong.
GMAT Club Bot
Re: If $20,000 were deposited into an account which yields x percent annua &nbs [#permalink] 03 Feb 2018, 21:23
Display posts from previous: Sort by

If $20,000 were deposited into an account which yields x percent annua

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


Copyright

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®.