Let amount be "X"


[X(1.08)^2 -x(1.08)] = 200 + x(1.08) - x

X(1.08)^2 - 2X(1.08) + X = 200

X[1.08^2 - 2*1.08 + 1] = 200

X[1.08-1]^2 = 200

X (.0064) = 200

X = 31250

sgr21 wrote:A man invested a certain sum of money at 8% compound interest compounded annually. While looking at his investment statement he realized that the interest he earned in the second year was $200 more than the interest he earned in the first year. What was the amount invested by him?
(A) $18,780
(B) $24,675
(C) $31,250
(D) $35,500

We can plug in the answers, which represent the amount invested.
Since the interest in the 2nd year increases by $200 -- a multiple of 100 -- 8% of the correct answer choice will almost certainly yield a very round number (such as a multiple of 10).
Thus, the correct answer choice is probably C or D.
Since the 8% interest rate is COMPOUNDED ANNUALLY, in the 2nd year the amount of interest increases by 8%.

C: 31,250
1st year interest = (.08)(31,250) = (8)(312,50) = 2500.
In the 2nd year, the increase in the amount of interest = (.08)(2500) = 200.
Success!

The correct answer is C.