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# A 2-year certificate of deposit is purchased for K dollars.

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Director
Joined: 17 Oct 2005
Posts: 889
A 2-year certificate of deposit is purchased for K dollars.  [#permalink]

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30 Nov 2005, 10:46
1
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Difficulty:

35% (medium)

Question Stats:

64% (01:03) correct 36% (00:57) wrong based on 377 sessions

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A 2-year certificate of deposit is purchased for K dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?

A. k(1.06)^2
B. k(1.06)^8
C. k(1.015)^2
D. k(1.015)^8
E. k(1.03)^4
SVP
Joined: 05 Apr 2005
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30 Nov 2005, 18:56
4
1
duttsit wrote:
christoph wrote:
D)...compund interest is: initial amount*(1+interest/x)^(time*x), where x is the number of times compunded annually

Agree.
k *(1 + 0.06/4) ^ (2 * 4)

annual interest rate (r) = 6%
term (n) = 2
value of k at the end of 2 yrs, if compounded annually=k(1+r)^n=k(1+0.06)^2

quaterly int. rate (r) = 1.5%
term (n) = 2x4 = 8
value of k at the end of 2 yrs, if compounded qtrly =k(1+r)^n=k(1+0.015)^8

so D.
##### General Discussion
Senior Manager
Joined: 11 Nov 2005
Posts: 313
Location: London

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30 Nov 2005, 10:49
B

k(1+0.06)^8

2 years = 8 times interest if paid quaterly
Director
Joined: 24 Oct 2005
Posts: 638
Location: London

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30 Nov 2005, 13:13
I am getting answer as A.
But there is definitely an easier method than what I have done
Senior Manager
Joined: 11 May 2004
Posts: 439
Location: New York

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30 Nov 2005, 13:23
I also got B

since it pays quarterly we take 4*2 (no of years) = 8
VP
Joined: 30 Sep 2004
Posts: 1448
Location: Germany

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30 Nov 2005, 13:39
2
D)...compund interest is: initial amount*(1+interest/x)^(time*x), where x is the number of times compunded annually
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Director
Joined: 17 Oct 2005
Posts: 889

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30 Nov 2005, 15:42
should we all memorize this compound interest fomula? or is it not necessary?
VP
Joined: 22 Aug 2005
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Location: CA

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30 Nov 2005, 15:56
joemama142000 wrote:
should we all memorize this compound interest fomula? or is it not necessary?

I would memorise it. A variation of it is used various contexts(eg money growing by 10% every year, mixture pbs etc)
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Director
Joined: 14 Sep 2005
Posts: 955
Location: South Korea

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30 Nov 2005, 19:10
joemama142000 wrote:
should we all memorize this compound interest fomula? or is it not necessary?

It is necessary.

I've taken the test yesterday, and one of the math questions required calculation of compound interest. Obviously, the formular was not given.
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GMAT Club Legend
Joined: 29 Jan 2005
Posts: 5062

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01 Dec 2005, 22:26
Got D as well. Just remember that with compound interest the # of compoundings must be multiplied to the # of years---> 4*2=8.

Between B and D, B fails to divide the interest rate (6%) by the compound (4). Therefore, it cannot be 1.06.

(D) by POE
Senior Manager
Joined: 15 Apr 2005
Posts: 410
Location: India, Chennai

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02 Dec 2005, 04:19
I think its good to know the formula for CI. The formula is
A=P(1+r/100)^n, Where P is the priniciple, R is the rate of interest, and n is the number of years.
In our case P =K, r = 6 and n = 8 (Since the interest is compounded quareterly, and for 2 years there are 8 quarters).

So it is K(1+6/100)^8
K(1.06)^8
GMAT Club Legend
Joined: 29 Jan 2005
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02 Dec 2005, 07:03
krisrini wrote:
I think its good to know the formula for CI. The formula is
A=P(1+r/100)^n, Where P is the priniciple, R is the rate of interest, and n is the number of years.
In our case P =K, r = 6 and n = 8 (Since the interest is compounded quareterly, and for 2 years there are 8 quarters).

So it is K(1+6/100)^8
K(1.06)^8

I think your formula is missing a few factors. We also must divide the interest rate by the # of compoundings per year (n) and multiply n by the number of years (y):

FV (future value)
P (principle)
r (interest rate expressed in decimal form)
n (number of compoundings)
t (time, in years)

FV=P(1+r/n)^t*n
Director
Joined: 24 Oct 2005
Posts: 638
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02 Dec 2005, 07:22
christoph wrote:
D)...compund interest is: initial amount*(1+interest/x)^(time*x), where x is the number of times compunded annually

If this is the formula for Compund Interest, we get interest as
k(1.015)^8
But we are asked the amount after two years isnt it.
Please can someone correct me where I am wrong.
SVP
Joined: 05 Apr 2005
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02 Dec 2005, 08:31
remgeo wrote:
christoph wrote:
D)...compund interest is: initial amount*(1+interest/x)^(time*x), where x is the number of times compunded annually

If this is the formula for Compund Interest, we get interest as
k(1.015)^8
But we are asked the amount after two years isnt it.
Please can someone correct me where I am wrong.

k is the initial amount. so end amount at the end of 2 years = k (1.015)^8
CEO
Joined: 21 Jan 2007
Posts: 2666
Location: New York City

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27 May 2007, 16:16
1
GMATT73 wrote:

We also must divide the interest rate by the # of compoundings per year (n) and multiply n by the number of years (y):

FV (future value)
P (principle)
r (interest rate expressed in decimal form)
n (number of compoundings)
t (time, in years)

FV=P(1+r/n)^t*n

yes this is the correct answer. its a very simple question.

FV=P(1+r/n)^t*n
k [1+ (6/4)] ^ (4*2)

k [1+ (.015)] ^8
therefore D
Intern
Joined: 09 May 2013
Posts: 15
Re: A 2-year certificate of deposit is purchased for K dollars.  [#permalink]

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18 Jan 2015, 07:01
joemama142000 wrote:
A 2-year certificate of deposit is purchased for K dollars. If the certificate earns interest at a n annual rate of 6 percent compound quarterly, which of the following represents the value, in dollars, of the certificate at the end of 2 years?

A. k(1.06)^2
B. k(1.06)^8
C. k(1.015)^2
D. k(1.015)^8
E. k(1.03)^4

Annual Rate of interest= 6%
Quaterly rate of interest= 6/4% = 1.5%

Now, periods of compounding in 2 years= 8 (8 quarters)
Thus k(1.015)^8

Intern
Joined: 19 Sep 2017
Posts: 1
Re: A 2-year certificate of deposit is purchased for K dollars.  [#permalink]

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05 Oct 2017, 06:34
I picked up initially on the fact that there are 2 years (or 8 quarters), but fell for the ANNUAL RATE of 1.06 because i forgot to divide that .06 interest rate by 4 quarters. Subtle.
Re: A 2-year certificate of deposit is purchased for K dollars. &nbs [#permalink] 05 Oct 2017, 06:34
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# A 2-year certificate of deposit is purchased for K dollars.

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