An investment increases 30 then drops 10 and then increases

An investment increases 30% then drops 10% and then increases 40%. What is the arithmetic mean of the returns? What is the compound rate of return and the total return on investment? please show full work thanks!

Solution

Let the initial investmennt be x.

It inncreased by 30%, so the innvestment has become 130*x/100=1.3x

And then it drop by 10%, so the investment has become 90*1.3x/100=1.17x

And then it inncrease by 40%, so the investment has become 140*1.17x/100=1.638x

Arithmetic mena of return is (1.638x-1x)*100/3=63.8%/3=21.26%

Compound rate of return is (1.638x-1x)*100=63.8%

Total return on investment is 1.638x