How good is your money maths?

The answer is C. The market stays the same.
First let me give you the numerical answer:

Option A. Rises 10%/year for 4 years then drops 10%/year for 4 years. END RESULT: 96% of the start value.
Option B. Falls 10%/year for 4 years then rises 10%/year for 4 years. END RESULT: 96% of the start value.
Option C. The market stays the same. END RESULT: 100% of the start value.
Option D. All the above answers are equal. NOT TRUE AS A, B & C produce different answers.

Now on to why:

The most important thing to understand is that if you add X% on a value then take X% off – you'll always end up with less than you started with.

If algebra is confusing lets try again this time with an example. You have £100 and get 20% on it. Now you've £120, but then you take 20% off that and (as 20% of £120 is £24) you've only £96 left.

The reason this works is because you're taking 20% off a bigger number than you're adding 20% too.

And this is commutative (it works both ways round) so let's do it the other way. You start with 100 and take 20% off, now you've £80, then you add 20% to £80 and you get £96. This is because again you're adding the 20% to a smaller number than you're taking it off.

Hope that helps. If you're not sure try it on a calculator yourself.