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.
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