Formula for raising rent but keeping tenant?

[Suzanne B.]

We bought a rental property in an artsy area that was undergoing a massive transition from being run-down to now a real hot-spot.  When it came time to list the property, not only were there few other renovated rentals on the market, but our property was about twice the size as the others, making it hard to guess fair market value.  Since renting it out, we've come to realize we really undervalued the rent price.  

I believe fair market price should be at least 20% more than we are charging.  However, I know that when our current tenants lease is up, it would be difficult to raise it that much and also keep them.  They aren't the best tenants, we're had some problems, nothing major, if we lost them I wouldn't be heartbroken.  But, that would mean a vacancy and losing rental income when vacant.  

Is there any sort of formula that investors have found that shows what % rent increase can/should be made if wanting to keep the tenant in place?  For example, has it been shown that tenants tend to agree with a 5% increase but not a 10%?  Or 10% is okay, but 20% causes them to move out?