Which of the following represents the profit...

[BTGmoderatorLU]

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

The OA is D.

I'm really confused with this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

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Hi LUANDATO,

We're asked to find the PROFIT from the investment of X dollars at N percent compound annual interest for 3 years. To answer this question, we need the Compound Interest Formula - we can then TEST VALUES. It's worth noting that the prompt asks for the PROFIT (NOT the TOTAL of the entire investment at the end of 3 years).

Compound Interest = (Principle)(1 + R)^T where R is the interest rate and T is the number of years.

IF....
X = $100 and N = 10, then the

Total investment at the end of 3 years = ($100)(1.1)^3

After subtracting out the original investment, the total PROFIT would be...

$100(1.1)^3 - $100

There's only one answer that matches...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[GMATWisdom]

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

The OA is D.

I'm really confused with this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

although option at D is as per the standard formula of compound interest, i shall do it for you using the simple interest formula and reach the result at D
amount after one year =x+nx/100=x(1+n/100)
amount after two years=
x(1+n/100)+ x(1+n/100)n/100
x(1+n/100)[(1+n/100)]= x(1+n/100)^2
amount after three years=
x(1+n/100)^2 + {x(1+n/100)^2}n/100
x(1+n/100)^2[(1+n/100)]
x(1+n/100)^3
interest = amount-principal
= x(1+n/100)^3 - x
Hence option D