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If $20,000 were deposited into an account which yields x percent annua [#permalink]
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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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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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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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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 NandishSSOver 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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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 Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app



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Re: If $20,000 were deposited into an account which yields x percent annua [#permalink]
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18 Jan 2018, 11:29
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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21 Jan 2018, 20:01
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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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..????? Sent from my BNDAL10 using GMAT Club Forum mobile app



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




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