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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

On the first of the year, James invested x dollars at [#permalink]

Show Tags

09 Mar 2012, 10:49

5

This post received KUDOS

11

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

56% (02:22) correct
44% (02:05) wrong based on 432 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?

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 . . .

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.

Re: On the first of the year, James invested x dollars at [#permalink]

Show Tags

15 Dec 2013, 17:49

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. _________________

On the first of the year, James invested x dollars at [#permalink]

Show Tags

09 Aug 2014, 09:59

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 . . .

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

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.

On the first of the year, James invested x dollars at [#permalink]

Show Tags

22 Jul 2015, 15:40

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

Re: On the first of the year, James invested x dollars at [#permalink]

Show Tags

29 Jul 2016, 12:19

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. _________________

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

As you leave central, bustling Tokyo and head Southwest the scenery gradually changes from urban to farmland. You go through a tunnel and on the other side all semblance...

Ghibli studio’s Princess Mononoke was my first exposure to Japan. I saw it at a sleepover with a neighborhood friend after playing some video games and I was...