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If $20,000 were deposited into an account which yields x percent annua

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If $20,000 were deposited into an account which yields x percent annua  [#permalink]

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New post 14 Jan 2018, 06:50
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If $20,000 were deposited into an account which yields x percent annua  [#permalink]

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New post 15 Jan 2018, 01:33
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)
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Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

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New post 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.
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Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

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New post 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!
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Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

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New post 15 Jan 2018, 06:49
Answer is:D

We can directly solve it by simply substituting values from choices

Tip always switch between sparse variables



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Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

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New post 18 Jan 2018, 11:29
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





You essentially have to work backwards from a simple compound interest question. What helped me was looking at the answer choices and doing trial and error from there. But there might be a better option?

If x% compounds quarterly it compounds every 3 months, hence it will compound twice after 6 months. If we use answer choice D, 8%, it compounds 4 times a year so it will compound at one fourth of its total interest.

So there will be a 2% increase each year. So hypothetically, we'd have to do 102% of 102% of 20,000.

100% of 20,000 = 20,000
1% of 20,000 = 200
1% again = 200
so 102% of 20,000 = 20,400

now, 102% of 20,400 = 20,808

Hence, D is correct
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Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

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New post 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

Answer: D
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Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

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New post 23 Jan 2018, 08:37
ScottTargetTestPrep 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


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

Answer: D

Hi scott

Here how to get sqrt 1.0404 without wasting time..?????

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Re: If $20,000 were deposited into an account which yields x percent annua  [#permalink]

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New post 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.
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Re: If $20,000 were deposited into an account which yields x percent annua   [#permalink] 03 Feb 2018, 21:23
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