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

It is currently 22 Feb 2019, 10:55

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

On the first of the year, James invested x dollars at

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

Hide Tags

 
Manager
Manager
avatar
Joined: 22 Jan 2012
Posts: 78
Location: India
Concentration: General Management, Technology
GPA: 3.3
WE: Engineering (Consulting)
On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 09 Mar 2012, 09:49
10
1
33
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

51% (02:11) correct 49% (02:46) wrong based on 980 sessions

HideShow timer Statistics

On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?

A. 2.04%
B. 6.12%
C. 8%
D. 8.25%
E. 10%

_________________

Press +1 Kudos rather than saying thanks
which is more helpful infact..

Ill be posting good questions as many as I can...

Towards Success

Most Helpful Expert Reply
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4486
Re: Interest problem  [#permalink]

Show Tags

New post 09 Mar 2012, 10:05
18
1
12
Hi, there. I'm happy to help with this. :)

Essentially, this question is asking for the effective interest rate.

So, every increase of 2% means we multiply x by the multiplier 1.02. The initial amount x gets multiplied by this multiply four times, one for each quarter, so . . .

y = x*(1.02)^4 = (1.08243216)*x ====> effective interest = 8.2432%

That's how you'd get the exact answer with a calculator, but of course you don't have a calculator available on GMAT PS questions. Think about it this way. With simple interest, 2% a quarter would add up to 8% annual. With compound interest, where you get interest on your interest, you will do a little better than you would with simple interest, so the answer should be something slightly above 8%. That leads us to . . .

Answer = D


Does that make sense? Please let me know if you have any additional questions on what I've said there.

Mike :)
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53066
Re: On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 09 Mar 2012, 10:17
13
9
iwillcrackgmat wrote:
On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?

A. 2.04%
B. 6.12%
C. 8%
D. 8.25%
E. 10%


If the interest were compounded annually instead of quarterly then in one year the interest would be 2*4=8%. Now, since the interest is compounded quarterly then there would be interest earned on interest (very small amount) thus the actual interest would be a little bit more than 8%, only answer choice D fits.

Answer: D.

Similar questions to practice:
jolene-entered-an-18-month-investment-contract-that-127308.html
marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.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

Intern
Intern
avatar
Joined: 29 Mar 2014
Posts: 5
GMAT ToolKit User
On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 09 Aug 2014, 08:59
mikemcgarry wrote:
Hi, there. I'm happy to help with this. :)

Essentially, this question is asking for the effective interest rate.

So, every increase of 2% means we multiply x by the multiplier 1.02. The initial amount x gets multiplied by this multiply four times, one for each quarter, so . . .

y = x*(1.02)^4 = (1.08243216)*x ====> effective interest = 8.2432%

That's how you'd get the exact answer with a calculator, but of course you don't have a calculator available on GMAT PS questions. Think about it this way. With simple interest, 2% a quarter would add up to 8% annual. With compound interest, where you get interest on your interest, you will do a little better than you would with simple interest, so the answer should be something slightly above 8%. That leads us to . . .

Answer = D


Does that make sense? Please let me know if you have any additional questions on what I've said there.
Mike :)



But according to compound interest formula y= x*( 1+ 0.02/4(quarterly)^time(1yr)*4(quarterly) -> so it comes to x* (1.02015). Please correct me where I'm going wrong.
Thanks
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4486
Re: On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 11 Aug 2014, 09:39
5
5
romeokillsu wrote:
But according to compound interest formula y= x*( 1+ 0.02/4(quarterly)^time(1yr)*4(quarterly) -> so it comes to x* (1.02015). Please correct me where I'm going wrong.
Thanks

Dear romeokillsu,
My friend, in most standard problems, the interest rate given is an ANNUAL interest rate, and for compounding quarterly, we have to divide it by four, as that formula does. BUT, in this problem we are told:

On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year.

So, this problem is following a different pattern --- it is not giving us an ANNUAL interest rate that needs to be divided by four. It is giving us a QUARTERLY interest rate.

That formulas you cited is only used when the problem gives us an annual interest rate. DO NOT blindly apply formulas! That is a recipe for failure! You must understand WHY the formula is true. You have to be able to recreate the argument whereby you derive the formula from scratch. That is really understanding, and that is what the GMAT is testing. Knowing just the formula and not where it comes from, not why it is true, is precisely the kind of superficial knowledge that the GMAT loves to exploit and punish.

For more on the compounding interest formula, see this blog:
http://magoosh.com/gmat/2014/compound-i ... -the-gmat/

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1820
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 11 Aug 2014, 23:06
2
Per quarter, interest = 2%

So for a year, interest = 8%

Due to quarter cummulation, effective yield (YTM) would be slight higher than 8%

Answer = 8.25% = D

Note: I've not made any calculations here; solved conceptually
_________________

Kindly press "+1 Kudos" to appreciate :)

Intern
Intern
User avatar
Status: casado
Joined: 26 Jan 2010
Posts: 16
Location: chile
WE 1:
WE 2:
WE 3:
On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 22 Jul 2015, 14:40
El ejercicio solicita comparar interés compuesto con interés simple:

Recordemos que:

1 trimestres = 3 meses, entonces 1 año = 4 trimestres = 12 meses.

Cuestión planteada por el ejercicio:

Cierta cantidad a un interes trimestral del 2%, pasado un año, debe ser igual a la misma cierta cantidad a la cuál se le aplica un interes desconocido (lo que se pregunta) anual. ¿ cuál es este último interés anual?

El interés del 2% trimestral, ya que involucra más de un período en el año, corresponde a interés compuesto, modelo
x(1 + 2/100)^4 = aproximadamente pero mayor que x(1 + o,o8).

Es decir la misma cierta cantidad a un interés anual cercano pero ligeramente mayor al 8% (interes simple), equivale a la cierta cantidad con un interés del 2% trimestral al finalizar una año (interés compuesto).

Respuesta Correcta D.
claudio hurtado
Tutor GMAT GRE MATH in Chile
www.gmatchile.cl
_________________

claudio hurtado maturana
Private lessons GMAT QUANT GRE QUANT SAT QUANT
Classes group of 6 students GMAT QUANT GRE QUANT SAT QUANT
Distance learning courses GMAT QUANT GRE QUANT SAT QUANT

Website http://www.gmatchile.cl
Whatsapp +56999410328
Email clasesgmatchile@gmail.com
Skype: clasesgmatchile@gmail.com
Address Avenida Hernando de Aguirre 128 Of 904, Tobalaba Metro Station, Santiago Chile.
Image

Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 373
Re: On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 06 Dec 2016, 21:00
Quarterly interest rate is not the same as annual interest rate compounded quarterly. We are given quarterly interest rate, therefore we do not need to divide by 4 in the compound interest formula.

ACCT A: x(1.02)^4=y
ACCT B: x(1+r)=y

x(1.02)^4=x(1+r)
(1.02)^4=(1+r)
0.0824=r

D.
Intern
Intern
avatar
S
Joined: 02 Jan 2017
Posts: 42
Location: India
Concentration: Leadership, Marketing
WE: Engineering (Telecommunications)
Re: On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 12 May 2017, 10:10
mikemcgarry wrote:
Hi, there. I'm happy to help with this. :)

Essentially, this question is asking for the effective interest rate.

So, every increase of 2% means we multiply x by the multiplier 1.02. The initial amount x gets multiplied by this multiply four times, one for each quarter, so . . .

y = x*(1.02)^4 = (1.08243216)*x ====> effective interest = 8.2432%

That's how you'd get the exact answer with a calculator, but of course you don't have a calculator available on GMAT PS questions. Think about it this way. With simple interest, 2% a quarter would add up to 8% annual. With compound interest, where you get interest on your interest, you will do a little better than you would with simple interest, so the answer should be something slightly above 8%. That leads us to . . .

Answer = D


Does that make sense? Please let me know if you have any additional questions on what I've said there.

Mike :)






Hi Mike,
I have a confusion here.Where in the question it is mentioned that we need to check t he COMPOUND INTEREST?

In QUESTION STEM
If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?

Here it says "interest rate /per year" Nowhere it us mentioned "Compounded annually"??

IN my opinion it should be Simple interest?No?
_________________

KUDOS PLEASE, If my post Helped you.
Thank you

Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4486
Re: On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 12 May 2017, 16:23
2
er.arun88 wrote:
Hi Mike,
I have a confusion here.Where in the question it is mentioned that we need to check t he COMPOUND INTEREST?

In QUESTION STEM
If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?

Here it says "interest rate /per year" Nowhere it us mentioned "Compounded annually"??

IN my opinion it should be Simple interest?No?

Dear er.arun88,

I'm happy to respond. :-)

There are two reasons why we can be 100% sure that compound interest in intended here.

1) The GMAT prepares you for the real business world and reflects the values of the real business world. Simple interest does not exist outside of kiddie math text books. No bank or credit card or financial institution on the planet would ever use simple interest: they all use compound interest. Thus, whenever the GMAT talks about interest and doesn't specify, we can be 100% sure that they mean compound interest. The GMAT would have to specify very clearly that they were using simple interest, although I don't know if I have ever even seen an official question about simple interest. It's true, the official GMAT is usually exceptionally clear, and probably would have said "compounds" rather than "yields" in the first sentence.

2) If there were no compounding, then in simple interest having the 2% interest accrue quarterly would make absolutely no sense, because by the end of the year, one would have exactly the same amount as an 8% annual account That essentially would be a question: do you know how to multiply by four? That is not the level at which the GMAT tests. The entire setup for the question is about measuring the compounding difference, and the subtle reasoning about how different the compound effects would be from the all-at-once interest payment is precisely what raises this question to the level of the conceptual complexity of the GMAT Quant section.

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Manager
Manager
avatar
B
Joined: 08 Jun 2017
Posts: 57
Re: On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 08 Jun 2017, 21:17
But here they are asking for rate in compund interest anually right , soit should be less than compounded monthly rate right? Please help me!!
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4486
Re: On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 09 Jun 2017, 15:04
1
Anazeer wrote:
But here they are asking for rate in compund interest anually right , soit should be less than compounded monthly rate right? Please help me!!

Dear Anazeer,

I'm happy to respond. :-)

When we have a quarterly interest rate, and these quarter compound, then over the course of a full year, the account makes a total amount of interested in the year that is more than it makes in any one quarter. Since all percentages are compared to the principal, which remains the same, the annual amount must be a larger percentage.

Does this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827
Re: On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 13 Jun 2017, 11:16
2
iwillcrackgmat wrote:
On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?

A. 2.04%
B. 6.12%
C. 8%
D. 8.25%
E. 10%


We can let James’ initial investment of x be $100. That is, we can say that James invested 100 dollars at Proudstar bank in an account that yields 2% in interest every quarter year. Recall the compound interest formula:

A = P(1 + i)^n

In which P = principal, i = interest rate per period, n = number of periods, and A = amount at the end of n periods.

Since a year has 4 quarters, n = 4 and we have:

A = 100(1 + 0.02)^4

A = 100(1.02)^4

A = 100(1.0824)

A = 108.24

We can see that he will get back $108.24 when the interest is compounded quarterly, and this has to be the value of y (if x = 100). So the question becomes: if James had invested $100 in an account that pays interest on a yearly basis, what must the interest rate be for James to have $108.24 at the end of the year?

We can use the same formula, except now we need to solve for i when n = 1:

108.24 = 100(1 + i)^1

1.0824 = 1 + i

0.0824 = i

8.24% = i

We see that the closest answer choice is D: 8.25%.

Alternate solution:

In this problem, we are given that a certain amount of money is being compounded quarterly with an interest rate of 2%. That is like paying an annual interest rate of 8% (4 x 0.02 = 0.08), but SOMEWHAT BETTER, since the interest is compounded (i.e., interest added on principal plus interest) every quarter of the year. So we are looking for an annual interest rate of slightly more than 8%. The only two answer choices that are more than 8% are 8.25% and 10%. Recall, we’ve said “somewhat better,” so it can’t be 10%. This leaves 8.25% as the most reasonable answer choice and the correct answer choice.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

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

Intern
Intern
avatar
B
Joined: 16 Oct 2017
Posts: 26
Location: India
GPA: 4
Re: On the first of the year, James invested x dollars at  [#permalink]

Show Tags

New post 30 Jan 2019, 19:46
JeffTargetTestPrep wrote:
iwillcrackgmat wrote:
On the first of the year, James invested x dollars at Proudstar bank in an account that yields 2% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?

A. 2.04%
B. 6.12%
C. 8%
D. 8.25%
E. 10%


We can let James’ initial investment of x be $100. That is, we can say that James invested 100 dollars at Proudstar bank in an account that yields 2% in interest every quarter year. Recall the compound interest formula:

A = P(1 + i)^n

In which P = principal, i = interest rate per period, n = number of periods, and A = amount at the end of n periods.

Since a year has 4 quarters, n = 4 and we have:

A = 100(1 + 0.02)^4

A = 100(1.02)^4

A = 100(1.0824)

A = 108.24

We can see that he will get back $108.24 when the interest is compounded quarterly, and this has to be the value of y (if x = 100). So the question becomes: if James had invested $100 in an account that pays interest on a yearly basis, what must the interest rate be for James to have $108.24 at the end of the year?

We can use the same formula, except now we need to solve for i when n = 1:

108.24 = 100(1 + i)^1

1.0824 = 1 + i

0.0824 = i

8.24% = i

We see that the closest answer choice is D: 8.25%.

Alternate solution:

In this problem, we are given that a certain amount of money is being compounded quarterly with an interest rate of 2%. That is like paying an annual interest rate of 8% (4 x 0.02 = 0.08), but SOMEWHAT BETTER, since the interest is compounded (i.e., interest added on principal plus interest) every quarter of the year. So we are looking for an annual interest rate of slightly more than 8%. The only two answer choices that are more than 8% are 8.25% and 10%. Recall, we’ve said “somewhat better,” so it can’t be 10%. This leaves 8.25% as the most reasonable answer choice and the correct answer choice.

Answer: D


Hello,

i have a doubt...shouldn't the "i" in the formula be divided by "n" as well where "n" is the number of times interest is compounded annually...and the answer comes out to be different in that case...please help me out

thanks in advance.
GMAT Club Bot
Re: On the first of the year, James invested x dollars at   [#permalink] 30 Jan 2019, 19:46
Display posts from previous: Sort by

On the first of the year, James invested x dollars at

  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®.