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

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

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09 Mar 2012, 09:49
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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%
[Reveal] Spoiler: OA

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09 Mar 2012, 10:05
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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 . . .

[Reveal] Spoiler:

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

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

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09 Mar 2012, 10:17
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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.

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

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15 Dec 2013, 16:49
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On the first of the year, James invested x dollars at [#permalink]

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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 . . .

[Reveal] Spoiler:

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

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11 Aug 2014, 09:39
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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
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Re: On the first of the year, James invested x dollars at [#permalink]

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11 Aug 2014, 19:04
yes . Thanks Mike.

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

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

So for a year, interest = 8%

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

Note: I've not made any calculations here; solved conceptually
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On the first of the year, James invested x dollars at [#permalink]

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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.

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

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29 Jul 2016, 11:19
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Re: On the first of the year, James invested x dollars at [#permalink]

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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.
Re: On the first of the year, James invested x dollars at   [#permalink] 06 Dec 2016, 21:00
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