Problem

After two consecutive years of $8 \%$ losses, what rate of return in the third year will produce a cumulative loss of $3 \%$ ? Note: Please make sure your final answer(s) are in percentage form and are accurate to 2 decimal places. For example $34.56 \%$. Rate of return $=0.00 \%$

Solution

Step 1 :Let's denote the initial value of the stock as \(x\). After the first year, the value of the stock becomes \(.92x\) due to the 8% loss.

Step 2 :After the second year, the value of the stock becomes \(.92 \times .92x = .8464x\) due to another 8% loss.

Step 3 :We want the value of the stock after the third year to be \(.97x\), which represents a cumulative loss of 3%.

Step 4 :Therefore, the rate of return in the third year should be \(.97x / .8464x - 1\).

Step 5 :Calculate the above expression, we get the rate of return in the third year is approximately \(0.1461\) or \(14.61\%\).

Step 6 :So, the rate of return in the third year that will produce a cumulative loss of 3% is \(\boxed{14.61\%}\).

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Source: https://solvelyapp.com/problems/17316/

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