A simple investment question.

[coopdog]

Hey guys an investment question,
If I earn 85% in year one but then lose 50% in year 2 what was my avarage percentage gain over the last two years?

Also does compounding effect the calculation?

Thanks guys!

[Sun Baked]

7.5% net loss over two years.

But compounding always affects the calculation...

[Vader]

Compounding would effect it, and I think you still be looking at a 15% gain or something, not sure though, that is a guess.

[MacAztec]

I think you lose a bit of money. Say you start with 1000 dollars.

85% gain, you are at $1,850 dollars. Then, year 2 comes, and you lose 50%...

That puts you at $925.

[Doctor Q]

I'll add my 2 cents worth.

MacAztec is right. You end up with $925.

Now you want to know the average percentage gain. I don't know the definition of this term, but my guess is that it means the percentage which, if it was applied each year with compounding, would produce the same result as your actual experience.

So you want to know what equivalent two-year rate of interest, call it p, would produce $925 from $1000 in two years, i.e., 1000 x p x p = 925, which you'd solve for p and get 0.96177, meaning you end up each year with about 96.177% of what you stared with, i.e., about a 3.823% loss.

Instead of starting from an assumed value ($1000) and the results of working out the final amount you have ($925), you could also compute the average percentage gain directly from the percentages given in the problem: squareroot(1.85 * 0.50) - 1 = 0.96177 - 1 = -0.03823.

So the average percentage gain is -3.823%, which you'd more likely call an average percentage loss of 3.823%.

We can check it. If we did things right, your two-year investment experience should produce the same result as a 3.823% loss each year, compounded.

Your results:
Start with $1000
Year 1: Earn 85% and you have $1850.00
Year 2: Lose 50% and you have $925.00

Using the average:
Start with $1000
Year 1: Lose 3.823% and you have $961.77
Year 2: Lose 3.823% and you have $925.00

And yes, compounding affects the calculation, because the interest you earn/lose each year depends on your balance, which depends on the interest earned the previous year.