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14 Jan 2018, 06:50
00:00

Difficulty:

75% (hard)

Question Stats:

60% (01:31) correct 40% (02:00) wrong based on 68 sessions

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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

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Joined: 26 Feb 2016
Posts: 2841
Location: India
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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 BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 2841 Location: India GPA: 3.12 Re: If$20,000 were deposited into an account which yields x percent annua [#permalink]

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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 Manager Joined: 07 Dec 2017 Posts: 72 Re: If$20,000 were deposited into an account which yields x percent annua [#permalink]

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15 Jan 2018, 06:49

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
Joined: 06 Oct 2017
Posts: 6

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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

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Manager
Joined: 26 Sep 2017
Posts: 91

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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.