I asked this question before, and got an answer, but I have a question about the response that was given.  The original question was:For an initial investment of 100, an investment yields returns of X1 and X2, where X1 and X2 are independent normal random variables with mean 60 and variance 25.  What is the probability that the rate of return of this investment is greater than 10%?In the answer that was given it says that the gain of the investment is X1+X2.  My question is why can we just group those together as one amount?  I was given a formula in my class that says the return on the investment would be the solution to the equation: -100+  X1/(1+r) +   X2/(1+r)2=0.  If this formula is used, a different solution would result for this problem.

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Asked Jun 6, 2019
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I asked this question before, and got an answer, but I have a question about the response that was given.  The original question was:

For an initial investment of 100, an investment yields returns of X1 and X2, where X1 and Xare independent normal random variables with mean 60 and variance 25.  What is the probability that the rate of return of this investment is greater than 10%?

In the answer that was given it says that the gain of the investment is X1+X2.  My question is why can we just group those together as one amount?  I was given a formula in my class that says the return on the investment would be the solution to the equation: -100+  X1/(1+r) +   X2/(1+r)2=0.  If this formula is used, a different solution would result for this problem.

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The formula that you shared from the text book is used for time-value-of-money calculations. Such a formula will be used when gains are received over specific periods ( say 2 years) . But the question...

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