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# Which of the following represents the profit from the investment of x

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
Which of the following represents the profit from the investment of x  [#permalink]

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23 Jul 2015, 03:22
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Difficulty:

5% (low)

Question Stats:

91% (01:06) correct 9% (01:11) wrong based on 64 sessions

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Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 3 years?

A. x(1 + 3n/100) – x
B. x(1 + n)^3/100 – x
C. 3x(1 + n/100)^2 – x
D. x(1 + n/100)^3 – x
E. x(1 + 3n/100)^3 – x

Kudos for a correct solution.

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Which of the following represents the profit from the investment of x  [#permalink]

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23 Jul 2015, 04:44
Bunuel wrote:
Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 3 years?

A. x(1 + 3n/100) – x
B. x(1 + n)^3/100 – x
C. 3x(1 + n/100)^2 – x
D. x(1 + n/100)^3 – x
E. x(1 + 3n/100)^3 – x

Kudos for a correct solution.

Amount after 3 years compounded yearly = x (1+n/100)^3

Thus profit = Final amount - original principle = x (1+n/100)^3 - x . Thus D is the correct answer.
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Which of the following represents the profit from the investment of x  [#permalink]

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23 Jul 2015, 06:03
Bunuel wrote:
Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 3 years?

A. x(1 + 3n/100) – x
B. x(1 + n)^3/100 – x
C. 3x(1 + n/100)^2 – x
D. x(1 + n/100)^3 – x
E. x(1 + 3n/100)^3 – x

Kudos for a correct solution.

Principle Sum = x
Rate of Interest = n% per annum compounded annually

Amount after 1 year = x + (n/100)x = x(1+ n/100)
Amount after 2 year = x(1+ n/100) + (n/100)*[x(1+ n/100)] = x(1+ n/100)^2
Amount after 3 year = x(1+ n/100)^2 + (n/100)*[x(1+ n/100)^2] = x(1+ n/100)^3

Interest After 3 Years = Amount After 3 Years - Principle
Interest After 3 Years = x(1+ n/100)^3 - x

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Re: Which of the following represents the profit from the investment of x  [#permalink]

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23 Jul 2015, 07:40
After 3 years the interest earned including the initial investment would be equal to $$x (1+n/100)^3$$. So, the interest earned = $$x (1+n/100)^3 - x$$. Ans (D).
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Re: Which of the following represents the profit from the investment of x  [#permalink]

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23 Jul 2015, 09:58
1
Bunuel wrote:
Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 3 years?

A. x(1 + 3n/100) – x
B. x(1 + n)^3/100 – x
C. 3x(1 + n/100)^2 – x
D. x(1 + n/100)^3 – x
E. x(1 + 3n/100)^3 – x

Kudos for a correct solution.

Formula for compound interest= Principal{(1+r/100)^n-1}
Using the formula above, profit/interest=x(1+n/100)^3-x
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Joined: 02 Sep 2009
Posts: 59587
Re: Which of the following represents the profit from the investment of x  [#permalink]

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26 Jul 2015, 12:13
Bunuel wrote:
Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 3 years?

A. x(1 + 3n/100) – x
B. x(1 + n)^3/100 – x
C. 3x(1 + n/100)^2 – x
D. x(1 + n/100)^3 – x
E. x(1 + 3n/100)^3 – x

Kudos for a correct solution.

800score Official Solution:

Compound interest is annually added to the principal sum. Therefore we can calculate the profit by deducting the original investment amount from the principal sum that we get in three years.

The principal sum increases by (1 + n/100) times each year. Therefore, in three years it increases by (1 + n/100)³ times. Since the original principal sum is x, then the profit is x(1 + n/100)³ – x.

The correct answer is choice (D).
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Re: Which of the following represents the profit from the investment of x   [#permalink] 26 Jul 2015, 12:13
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