If the account is down 20%, what rate of return over the next year do we need to get to be even, in other words make back the 20% we lost? The rate of inflation in this case is zero.
25% return as what you'd want to do is invert the 80% that is left to get the figure. Thus, just compute .8^-1=1.25 or 25%.
Now, to walk this through in a bit more detail for those that found the above to be a bit mystical:
- Consider starting with $100 and we want to end with $100.
- Now, the account goes down 20% which means that we are at $80 as 100*(1-.20)=80.
- Now, to get an addition $20 back, we could take the fraction 20/80=1/4=.25 or 25% as you want to get a quarter back to get whole again.