SOLUTION: After two consecutive years of 10% losses, what rate of return in the third year will produce a cumulative loss of 30%? (Round your answer to 2 decimal places. Negative answers sho

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Question 908648: After two consecutive years of 10% losses, what rate of return in the third year will produce a cumulative loss of 30%? (Round your answer to 2 decimal places. Negative answers should be indicated by minus sign.)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
After two consecutive years of 10% losses, what rate of return in the third year will produce a cumulative loss of 30%? (Round your answer to 2 decimal places. Negative answers should be indicated by minus sign.)
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Start with "x" dollars.
After one year you have 0.9x
After two years you have 0.9^2x = 0.81x
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Equation:
If your interest loss is "k%" you have (1-k)% of the 2nd year's balance.
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0.70x = (1-k)(0.81x)
1-k = 0.70/0.81 = 0.86
k = 0.14%
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Cheers,
Stan H.